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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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||