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Groups of prime power order . Volume 2 [[electronic resource] /] / by Yakov Berkovich and Zvonimir Janko
Groups of prime power order . Volume 2 [[electronic resource] /] / by Yakov Berkovich and Zvonimir Janko
Autore Berkovich Yakov
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (612 p.)
Disciplina 512.23
Altri autori (Persone) JankoZvonimir
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
Soggetto genere / forma Electronic books.
ISBN 1-281-99348-4
9786611993481
3-11-916239-6
3-11-020823-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Preface -- §46. Degrees of irreducible characters of Suzuki p-groups -- §47. On the number of metacyclic epimorphic images of finite p-groups -- §48. On 2-groups with small centralizer of an involution, I -- §49. On 2-groups with small centralizer of an involution, II -- §50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8 -- §51. 2-groups with self centralizing subgroup isomorphic to E8 -- §52. 2-groups with 2-subgroup of small order -- §53. 2-groups G with c2(G) = 4 -- §54. 2-groups G with cn(G) = 4, n > 2 -- §55. 2-groups G with small subgroup (x ∈ G | o(x) = 2") -- §56. Theorem of Ward on quaternion-free 2-groups -- §57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4 -- §58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate -- §59. p-groups with few nonnormal subgroups -- §60. The structure of the Burnside group of order 212 -- §61. Groups of exponent 4 generated by three involutions -- §62. Groups with large normal closures of nonnormal cyclic subgroups -- §63. Groups all of whose cyclic subgroups of composite orders are normal -- §64. p-groups generated by elements of given order -- §65. A2-groups -- §66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups -- §67. Determination of U2-groups -- §68. Characterization of groups of prime exponent -- §69. Elementary proofs of some Blackburn's theorems -- §70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator -- §71. Determination of A2-groups -- §72. An-groups, n > 2 -- §73. Classification of modular p-groups -- §74. p-groups with a cyclic subgroup of index p2 -- §75. Elements of order ≤ in p-groups -- §76. p-groups with few A1-subgroups -- §77. 2-groups with a self-centralizing abelian subgroup of type (4, 2) -- §78. Minimal nonmodular p-groups -- §79. Nonmodular quaternion-free 2-groups -- §80. Minimal non-quaternion-free 2-groups -- §81. Maximal abelian subgroups in 2-groups -- §82. A classification of 2-groups with exactly three involutions -- §83. p-groups G with Ω2(G) or Ω2*(G) extraspecial -- §84. 2-groups whose nonmetacyclic subgroups are generated by involutions -- §85. 2-groups with a nonabelian Frattini subgroup of order 16 -- §86. p-groups G with metacyclic Ω2*(G) -- §87. 2-groups with exactly one nonmetacyclic maximal subgroup -- §88. Hall chains in normal subgroups of p-groups -- §89. 2-groups with exactly six cyclic subgroups of order 4 -- §90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8 -- §91. Maximal abelian subgroups of p-groups -- §92. On minimal nonabelian subgroups of p-groups -- Appendix 16. Some central products -- Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results -- Appendix 18. Replacement theorems -- Appendix 19. New proof of Ward's theorem on quaternion-free 2-groups -- Appendix 20. Some remarks on automorphisms -- Appendix 21. Isaacs' examples -- Appendix 22. Minimal nonnilpotent groups -- Appendix 23. Groups all of whose noncentral conjugacy classes have the same size -- Appendix 24. On modular 2-groups -- Appendix 25. Schreier's inequality for p-groups -- Appendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class -- Research problems and themes II -- Backmatter
Record Nr. UNINA-9910454598903321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 1 [[electronic resource] /] / by Yakov Berkovich
Groups of prime power order . Volume 1 [[electronic resource] /] / by Yakov Berkovich
Autore Berkovich Yakov
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (532 p.)
Disciplina 512.23
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
Soggetto genere / forma Electronic books.
ISBN 1-281-99347-6
9786611993474
3-11-020822-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Foreword -- Preface -- Introduction -- §1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia -- §2. The class number, character degrees -- §3. Minimal classes -- §4. p-groups with cyclic Frattini subgroup -- §5. Hall's enumeration principle -- §6. q'-automorphisms of q-groups -- §7. Regular p-groups -- §8. Pyramidal p-groups -- §9. On p-groups of maximal class -- §10. On abelian subgroups of p-groups -- §11. On the power structure of a p-group -- §12. Counting theorems for p-groups of maximal class -- §13. Further counting theorems -- §14. Thompson's critical subgroup -- §15. Generators of p-groups -- §16. Classification of finite p-groups all of whose noncyclic subgroups are normal -- §17. Counting theorems for regular p-groups -- §18. Counting theorems for irregular p-groups -- §19. Some additional counting theorems -- §20. Groups with small abelian subgroups and partitions -- §21. On the Schur multiplier and the commutator subgroup -- §22. On characters of p-groups -- §23. On subgroups of given exponent -- §24. Hall's theorem on normal subgroups of given exponent -- §25. On the lattice of subgroups of a group -- §26. Powerful p-groups -- §27. p-groups with normal centralizers of all elements -- §28. p-groups with a uniqueness condition for nonnormal subgroups -- §29. On isoclinism -- §30. On p-groups with few nonabelian subgroups of order pp and exponent p -- §31. On p-groups with small p0-groups of operators -- §32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups -- §33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3 -- §34. Nilpotent groups of automorphisms -- §35. Maximal abelian subgroups of p-groups -- §36. Short proofs of some basic characterization theorems of finite p-group theory -- §37. MacWilliams' theorem -- §38. p-groups with exactly two conjugate classes of subgroups of small orders and exponentp > 2 -- §39. Alperin's problem on abelian subgroups of small index -- §40. On breadth and class number of p-groups -- §41. Groups in which every two noncyclic subgroups of the same order have the same rank -- §42. On intersections of some subgroups -- §43. On 2-groups with few cyclic subgroups of given order -- §44. Some characterizations of metacyclic p-groups -- §45. A counting theorem for p-groups of odd order -- Appendix 1. The Hall-Petrescu formula -- Appendix 2. Mann's proof of monomiality of p-groups -- Appendix 3. Theorems of Isaacs on actions of groups -- Appendix 4. Freiman's number-theoretical theorems -- Appendix 5. Another proof of Theorem 5.4 -- Appendix 6. On the order of p-groups of given derived length -- Appendix 7. Relative indices of elements of p-groups -- Appendix 8. p-groups withabsolutely regular Frattini subgroup -- Appendix 9. On characteristic subgroups of metacyclic groups -- Appendix 10. On minimal characters of p-groups -- Appendix 11. On sums of degrees of irreducible characters -- Appendix 12. 2-groups whose maximal cyclic subgroups of order > 2 are self-centralizing -- Appendix 13. Normalizers of Sylow p-subgroups of symmetric groups -- Appendix 14. 2-groups with an involution contained in only one subgroup of order 4 -- Appendix 15. A criterion for a group to be nilpotent -- Research problems and themes I -- Backmatter
Record Nr. UNINA-9910454598003321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 1 [[electronic resource] /] / by Yakov Berkovich
Groups of prime power order . Volume 1 [[electronic resource] /] / by Yakov Berkovich
Autore Berkovich Yakov
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (532 p.)
Disciplina 512.23
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
Soggetto non controllato Group Theory
Order
Primes
ISBN 1-281-99347-6
9786611993474
3-11-020822-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Foreword -- Preface -- Introduction -- §1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia -- §2. The class number, character degrees -- §3. Minimal classes -- §4. p-groups with cyclic Frattini subgroup -- §5. Hall's enumeration principle -- §6. q'-automorphisms of q-groups -- §7. Regular p-groups -- §8. Pyramidal p-groups -- §9. On p-groups of maximal class -- §10. On abelian subgroups of p-groups -- §11. On the power structure of a p-group -- §12. Counting theorems for p-groups of maximal class -- §13. Further counting theorems -- §14. Thompson's critical subgroup -- §15. Generators of p-groups -- §16. Classification of finite p-groups all of whose noncyclic subgroups are normal -- §17. Counting theorems for regular p-groups -- §18. Counting theorems for irregular p-groups -- §19. Some additional counting theorems -- §20. Groups with small abelian subgroups and partitions -- §21. On the Schur multiplier and the commutator subgroup -- §22. On characters of p-groups -- §23. On subgroups of given exponent -- §24. Hall's theorem on normal subgroups of given exponent -- §25. On the lattice of subgroups of a group -- §26. Powerful p-groups -- §27. p-groups with normal centralizers of all elements -- §28. p-groups with a uniqueness condition for nonnormal subgroups -- §29. On isoclinism -- §30. On p-groups with few nonabelian subgroups of order pp and exponent p -- §31. On p-groups with small p0-groups of operators -- §32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups -- §33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3 -- §34. Nilpotent groups of automorphisms -- §35. Maximal abelian subgroups of p-groups -- §36. Short proofs of some basic characterization theorems of finite p-group theory -- §37. MacWilliams' theorem -- §38. p-groups with exactly two conjugate classes of subgroups of small orders and exponentp > 2 -- §39. Alperin's problem on abelian subgroups of small index -- §40. On breadth and class number of p-groups -- §41. Groups in which every two noncyclic subgroups of the same order have the same rank -- §42. On intersections of some subgroups -- §43. On 2-groups with few cyclic subgroups of given order -- §44. Some characterizations of metacyclic p-groups -- §45. A counting theorem for p-groups of odd order -- Appendix 1. The Hall-Petrescu formula -- Appendix 2. Mann's proof of monomiality of p-groups -- Appendix 3. Theorems of Isaacs on actions of groups -- Appendix 4. Freiman's number-theoretical theorems -- Appendix 5. Another proof of Theorem 5.4 -- Appendix 6. On the order of p-groups of given derived length -- Appendix 7. Relative indices of elements of p-groups -- Appendix 8. p-groups withabsolutely regular Frattini subgroup -- Appendix 9. On characteristic subgroups of metacyclic groups -- Appendix 10. On minimal characters of p-groups -- Appendix 11. On sums of degrees of irreducible characters -- Appendix 12. 2-groups whose maximal cyclic subgroups of order > 2 are self-centralizing -- Appendix 13. Normalizers of Sylow p-subgroups of symmetric groups -- Appendix 14. 2-groups with an involution contained in only one subgroup of order 4 -- Appendix 15. A criterion for a group to be nilpotent -- Research problems and themes I -- Backmatter
Record Nr. UNINA-9910782769703321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 2 [[electronic resource] /] / by Yakov Berkovich and Zvonimir Janko
Groups of prime power order . Volume 2 [[electronic resource] /] / by Yakov Berkovich and Zvonimir Janko
Autore Berkovich Yakov
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (612 p.)
Disciplina 512.23
Altri autori (Persone) JankoZvonimir
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
Soggetto non controllato Group Theory
Order
Primes
ISBN 1-281-99348-4
9786611993481
3-11-916239-6
3-11-020823-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Preface -- §46. Degrees of irreducible characters of Suzuki p-groups -- §47. On the number of metacyclic epimorphic images of finite p-groups -- §48. On 2-groups with small centralizer of an involution, I -- §49. On 2-groups with small centralizer of an involution, II -- §50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8 -- §51. 2-groups with self centralizing subgroup isomorphic to E8 -- §52. 2-groups with 2-subgroup of small order -- §53. 2-groups G with c2(G) = 4 -- §54. 2-groups G with cn(G) = 4, n > 2 -- §55. 2-groups G with small subgroup (x ∈ G | o(x) = 2") -- §56. Theorem of Ward on quaternion-free 2-groups -- §57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4 -- §58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate -- §59. p-groups with few nonnormal subgroups -- §60. The structure of the Burnside group of order 212 -- §61. Groups of exponent 4 generated by three involutions -- §62. Groups with large normal closures of nonnormal cyclic subgroups -- §63. Groups all of whose cyclic subgroups of composite orders are normal -- §64. p-groups generated by elements of given order -- §65. A2-groups -- §66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups -- §67. Determination of U2-groups -- §68. Characterization of groups of prime exponent -- §69. Elementary proofs of some Blackburn's theorems -- §70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator -- §71. Determination of A2-groups -- §72. An-groups, n > 2 -- §73. Classification of modular p-groups -- §74. p-groups with a cyclic subgroup of index p2 -- §75. Elements of order ≤ in p-groups -- §76. p-groups with few A1-subgroups -- §77. 2-groups with a self-centralizing abelian subgroup of type (4, 2) -- §78. Minimal nonmodular p-groups -- §79. Nonmodular quaternion-free 2-groups -- §80. Minimal non-quaternion-free 2-groups -- §81. Maximal abelian subgroups in 2-groups -- §82. A classification of 2-groups with exactly three involutions -- §83. p-groups G with Ω2(G) or Ω2*(G) extraspecial -- §84. 2-groups whose nonmetacyclic subgroups are generated by involutions -- §85. 2-groups with a nonabelian Frattini subgroup of order 16 -- §86. p-groups G with metacyclic Ω2*(G) -- §87. 2-groups with exactly one nonmetacyclic maximal subgroup -- §88. Hall chains in normal subgroups of p-groups -- §89. 2-groups with exactly six cyclic subgroups of order 4 -- §90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8 -- §91. Maximal abelian subgroups of p-groups -- §92. On minimal nonabelian subgroups of p-groups -- Appendix 16. Some central products -- Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results -- Appendix 18. Replacement theorems -- Appendix 19. New proof of Ward's theorem on quaternion-free 2-groups -- Appendix 20. Some remarks on automorphisms -- Appendix 21. Isaacs' examples -- Appendix 22. Minimal nonnilpotent groups -- Appendix 23. Groups all of whose noncentral conjugacy classes have the same size -- Appendix 24. On modular 2-groups -- Appendix 25. Schreier's inequality for p-groups -- Appendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class -- Research problems and themes II -- Backmatter
Record Nr. UNINA-9910782769603321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 1 / / by Yakov Berkovich
Groups of prime power order . Volume 1 / / by Yakov Berkovich
Autore Berkovich Yakov
Edizione [1st ed.]
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (532 p.)
Disciplina 512.23
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
ISBN 9786611993474
9781281993472
1281993476
9783110208221
3110208229
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Foreword -- Preface -- Introduction -- §1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia -- §2. The class number, character degrees -- §3. Minimal classes -- §4. p-groups with cyclic Frattini subgroup -- §5. Hall's enumeration principle -- §6. q'-automorphisms of q-groups -- §7. Regular p-groups -- §8. Pyramidal p-groups -- §9. On p-groups of maximal class -- §10. On abelian subgroups of p-groups -- §11. On the power structure of a p-group -- §12. Counting theorems for p-groups of maximal class -- §13. Further counting theorems -- §14. Thompson's critical subgroup -- §15. Generators of p-groups -- §16. Classification of finite p-groups all of whose noncyclic subgroups are normal -- §17. Counting theorems for regular p-groups -- §18. Counting theorems for irregular p-groups -- §19. Some additional counting theorems -- §20. Groups with small abelian subgroups and partitions -- §21. On the Schur multiplier and the commutator subgroup -- §22. On characters of p-groups -- §23. On subgroups of given exponent -- §24. Hall's theorem on normal subgroups of given exponent -- §25. On the lattice of subgroups of a group -- §26. Powerful p-groups -- §27. p-groups with normal centralizers of all elements -- §28. p-groups with a uniqueness condition for nonnormal subgroups -- §29. On isoclinism -- §30. On p-groups with few nonabelian subgroups of order pp and exponent p -- §31. On p-groups with small p0-groups of operators -- §32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups -- §33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3 -- §34. Nilpotent groups of automorphisms -- §35. Maximal abelian subgroups of p-groups -- §36. Short proofs of some basic characterization theorems of finite p-group theory -- §37. MacWilliams' theorem -- §38. p-groups with exactly two conjugate classes of subgroups of small orders and exponentp > 2 -- §39. Alperin's problem on abelian subgroups of small index -- §40. On breadth and class number of p-groups -- §41. Groups in which every two noncyclic subgroups of the same order have the same rank -- §42. On intersections of some subgroups -- §43. On 2-groups with few cyclic subgroups of given order -- §44. Some characterizations of metacyclic p-groups -- §45. A counting theorem for p-groups of odd order -- Appendix 1. The Hall-Petrescu formula -- Appendix 2. Mann's proof of monomiality of p-groups -- Appendix 3. Theorems of Isaacs on actions of groups -- Appendix 4. Freiman's number-theoretical theorems -- Appendix 5. Another proof of Theorem 5.4 -- Appendix 6. On the order of p-groups of given derived length -- Appendix 7. Relative indices of elements of p-groups -- Appendix 8. p-groups withabsolutely regular Frattini subgroup -- Appendix 9. On characteristic subgroups of metacyclic groups -- Appendix 10. On minimal characters of p-groups -- Appendix 11. On sums of degrees of irreducible characters -- Appendix 12. 2-groups whose maximal cyclic subgroups of order > 2 are self-centralizing -- Appendix 13. Normalizers of Sylow p-subgroups of symmetric groups -- Appendix 14. 2-groups with an involution contained in only one subgroup of order 4 -- Appendix 15. A criterion for a group to be nilpotent -- Research problems and themes I -- Backmatter
Record Nr. UNINA-9911098419403321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 2 / / by Yakov Berkovich and Zvonimir Janko
Groups of prime power order . Volume 2 / / by Yakov Berkovich and Zvonimir Janko
Autore Berkovich Yakov
Edizione [1st ed.]
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (612 p.)
Disciplina 512.23
Altri autori (Persone) JankoZvonimir
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
ISBN 9786611993481
9781281993489
1281993484
9783119162395
3119162396
9783110208238
3110208237
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Preface -- §46. Degrees of irreducible characters of Suzuki p-groups -- §47. On the number of metacyclic epimorphic images of finite p-groups -- §48. On 2-groups with small centralizer of an involution, I -- §49. On 2-groups with small centralizer of an involution, II -- §50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8 -- §51. 2-groups with self centralizing subgroup isomorphic to E8 -- §52. 2-groups with 2-subgroup of small order -- §53. 2-groups G with c2(G) = 4 -- §54. 2-groups G with cn(G) = 4, n > 2 -- §55. 2-groups G with small subgroup (x ∈ G | o(x) = 2") -- §56. Theorem of Ward on quaternion-free 2-groups -- §57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4 -- §58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate -- §59. p-groups with few nonnormal subgroups -- §60. The structure of the Burnside group of order 212 -- §61. Groups of exponent 4 generated by three involutions -- §62. Groups with large normal closures of nonnormal cyclic subgroups -- §63. Groups all of whose cyclic subgroups of composite orders are normal -- §64. p-groups generated by elements of given order -- §65. A2-groups -- §66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups -- §67. Determination of U2-groups -- §68. Characterization of groups of prime exponent -- §69. Elementary proofs of some Blackburn's theorems -- §70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator -- §71. Determination of A2-groups -- §72. An-groups, n > 2 -- §73. Classification of modular p-groups -- §74. p-groups with a cyclic subgroup of index p2 -- §75. Elements of order ≤ in p-groups -- §76. p-groups with few A1-subgroups -- §77. 2-groups with a self-centralizing abelian subgroup of type (4, 2) -- §78. Minimal nonmodular p-groups -- §79. Nonmodular quaternion-free 2-groups -- §80. Minimal non-quaternion-free 2-groups -- §81. Maximal abelian subgroups in 2-groups -- §82. A classification of 2-groups with exactly three involutions -- §83. p-groups G with Ω2(G) or Ω2*(G) extraspecial -- §84. 2-groups whose nonmetacyclic subgroups are generated by involutions -- §85. 2-groups with a nonabelian Frattini subgroup of order 16 -- §86. p-groups G with metacyclic Ω2*(G) -- §87. 2-groups with exactly one nonmetacyclic maximal subgroup -- §88. Hall chains in normal subgroups of p-groups -- §89. 2-groups with exactly six cyclic subgroups of order 4 -- §90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8 -- §91. Maximal abelian subgroups of p-groups -- §92. On minimal nonabelian subgroups of p-groups -- Appendix 16. Some central products -- Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results -- Appendix 18. Replacement theorems -- Appendix 19. New proof of Ward's theorem on quaternion-free 2-groups -- Appendix 20. Some remarks on automorphisms -- Appendix 21. Isaacs' examples -- Appendix 22. Minimal nonnilpotent groups -- Appendix 23. Groups all of whose noncentral conjugacy classes have the same size -- Appendix 24. On modular 2-groups -- Appendix 25. Schreier's inequality for p-groups -- Appendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class -- Research problems and themes II -- Backmatter
Record Nr. UNINA-9911107293703321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Groups of prime power order . Volume 1 / / by Yakov Berkovich
Groups of prime power order . Volume 1 / / by Yakov Berkovich
Autore Berkovich Yakov
Edizione [1st ed.]
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (532 p.)
Disciplina 512.23
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
ISBN 9786611993474
9781281993472
1281993476
9783110208221
3110208229
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Foreword -- Preface -- Introduction -- §1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia -- §2. The class number, character degrees -- §3. Minimal classes -- §4. p-groups with cyclic Frattini subgroup -- §5. Hall's enumeration principle -- §6. q'-automorphisms of q-groups -- §7. Regular p-groups -- §8. Pyramidal p-groups -- §9. On p-groups of maximal class -- §10. On abelian subgroups of p-groups -- §11. On the power structure of a p-group -- §12. Counting theorems for p-groups of maximal class -- §13. Further counting theorems -- §14. Thompson's critical subgroup -- §15. Generators of p-groups -- §16. Classification of finite p-groups all of whose noncyclic subgroups are normal -- §17. Counting theorems for regular p-groups -- §18. Counting theorems for irregular p-groups -- §19. Some additional counting theorems -- §20. Groups with small abelian subgroups and partitions -- §21. On the Schur multiplier and the commutator subgroup -- §22. On characters of p-groups -- §23. On subgroups of given exponent -- §24. Hall's theorem on normal subgroups of given exponent -- §25. On the lattice of subgroups of a group -- §26. Powerful p-groups -- §27. p-groups with normal centralizers of all elements -- §28. p-groups with a uniqueness condition for nonnormal subgroups -- §29. On isoclinism -- §30. On p-groups with few nonabelian subgroups of order pp and exponent p -- §31. On p-groups with small p0-groups of operators -- §32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups -- §33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3 -- §34. Nilpotent groups of automorphisms -- §35. Maximal abelian subgroups of p-groups -- §36. Short proofs of some basic characterization theorems of finite p-group theory -- §37. MacWilliams' theorem -- §38. p-groups with exactly two conjugate classes of subgroups of small orders and exponentp > 2 -- §39. Alperin's problem on abelian subgroups of small index -- §40. On breadth and class number of p-groups -- §41. Groups in which every two noncyclic subgroups of the same order have the same rank -- §42. On intersections of some subgroups -- §43. On 2-groups with few cyclic subgroups of given order -- §44. Some characterizations of metacyclic p-groups -- §45. A counting theorem for p-groups of odd order -- Appendix 1. The Hall-Petrescu formula -- Appendix 2. Mann's proof of monomiality of p-groups -- Appendix 3. Theorems of Isaacs on actions of groups -- Appendix 4. Freiman's number-theoretical theorems -- Appendix 5. Another proof of Theorem 5.4 -- Appendix 6. On the order of p-groups of given derived length -- Appendix 7. Relative indices of elements of p-groups -- Appendix 8. p-groups withabsolutely regular Frattini subgroup -- Appendix 9. On characteristic subgroups of metacyclic groups -- Appendix 10. On minimal characters of p-groups -- Appendix 11. On sums of degrees of irreducible characters -- Appendix 12. 2-groups whose maximal cyclic subgroups of order > 2 are self-centralizing -- Appendix 13. Normalizers of Sylow p-subgroups of symmetric groups -- Appendix 14. 2-groups with an involution contained in only one subgroup of order 4 -- Appendix 15. A criterion for a group to be nilpotent -- Research problems and themes I -- Backmatter
Record Nr. UNINA-9911144360903321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Groups of prime power order . Volume 2 / / by Yakov Berkovich and Zvonimir Janko
Groups of prime power order . Volume 2 / / by Yakov Berkovich and Zvonimir Janko
Autore Berkovich Yakov
Edizione [1st ed.]
Pubbl/distr/stampa Berlin ; ; New York, : W. de Gruyter, c2008
Descrizione fisica 1 online resource (612 p.)
Disciplina 512.23
Altri autori (Persone) JankoZvonimir
Collana De Gruyter expositions in mathematics
Soggetto topico Finite groups
Group theory
ISBN 9786611993481
9781281993489
1281993484
9783119162395
3119162396
9783110208238
3110208237
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Frontmatter -- Contents -- List of definitions and notations -- Preface -- §46. Degrees of irreducible characters of Suzuki p-groups -- §47. On the number of metacyclic epimorphic images of finite p-groups -- §48. On 2-groups with small centralizer of an involution, I -- §49. On 2-groups with small centralizer of an involution, II -- §50. Janko's theorem on 2-groups without normal elementary abelian subgroups of order 8 -- §51. 2-groups with self centralizing subgroup isomorphic to E8 -- §52. 2-groups with 2-subgroup of small order -- §53. 2-groups G with c2(G) = 4 -- §54. 2-groups G with cn(G) = 4, n > 2 -- §55. 2-groups G with small subgroup (x ∈ G | o(x) = 2") -- §56. Theorem of Ward on quaternion-free 2-groups -- §57. Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic and have exponent 4 -- §58. Non-Dedekindian p-groups all of whose nonnormal subgroups of the same order are conjugate -- §59. p-groups with few nonnormal subgroups -- §60. The structure of the Burnside group of order 212 -- §61. Groups of exponent 4 generated by three involutions -- §62. Groups with large normal closures of nonnormal cyclic subgroups -- §63. Groups all of whose cyclic subgroups of composite orders are normal -- §64. p-groups generated by elements of given order -- §65. A2-groups -- §66. A new proof of Blackburn's theorem on minimal nonmetacyclic 2-groups -- §67. Determination of U2-groups -- §68. Characterization of groups of prime exponent -- §69. Elementary proofs of some Blackburn's theorems -- §70. Non-2-generator p-groups all of whose maximal subgroups are 2-generator -- §71. Determination of A2-groups -- §72. An-groups, n > 2 -- §73. Classification of modular p-groups -- §74. p-groups with a cyclic subgroup of index p2 -- §75. Elements of order ≤ in p-groups -- §76. p-groups with few A1-subgroups -- §77. 2-groups with a self-centralizing abelian subgroup of type (4, 2) -- §78. Minimal nonmodular p-groups -- §79. Nonmodular quaternion-free 2-groups -- §80. Minimal non-quaternion-free 2-groups -- §81. Maximal abelian subgroups in 2-groups -- §82. A classification of 2-groups with exactly three involutions -- §83. p-groups G with Ω2(G) or Ω2*(G) extraspecial -- §84. 2-groups whose nonmetacyclic subgroups are generated by involutions -- §85. 2-groups with a nonabelian Frattini subgroup of order 16 -- §86. p-groups G with metacyclic Ω2*(G) -- §87. 2-groups with exactly one nonmetacyclic maximal subgroup -- §88. Hall chains in normal subgroups of p-groups -- §89. 2-groups with exactly six cyclic subgroups of order 4 -- §90. Nonabelian 2-groups all of whose minimal nonabelian subgroups are of order 8 -- §91. Maximal abelian subgroups of p-groups -- §92. On minimal nonabelian subgroups of p-groups -- Appendix 16. Some central products -- Appendix 17. Alternate proofs of characterization theorems of Miller and Janko on 2-groups, and some related results -- Appendix 18. Replacement theorems -- Appendix 19. New proof of Ward's theorem on quaternion-free 2-groups -- Appendix 20. Some remarks on automorphisms -- Appendix 21. Isaacs' examples -- Appendix 22. Minimal nonnilpotent groups -- Appendix 23. Groups all of whose noncentral conjugacy classes have the same size -- Appendix 24. On modular 2-groups -- Appendix 25. Schreier's inequality for p-groups -- Appendix 26. p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class -- Research problems and themes II -- Backmatter
Record Nr. UNINA-9911144360703321
Berkovich Yakov  
Berlin ; ; New York, : W. de Gruyter, c2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui