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Finite groups whose 2-subgroups are generated by at most 4 elements / / [by] Daniel Gorenstein and Koichiro Harada
| Finite groups whose 2-subgroups are generated by at most 4 elements / / [by] Daniel Gorenstein and Koichiro Harada |
| Autore | Gorenstein Daniel |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 1974 |
| Descrizione fisica | 1 online resource (473 p.) |
| Disciplina | 512/.2 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Finite groups |
| ISBN | 0-8218-9947-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""TABLE OF CONTENTS""; ""INTRODUCTION""; ""PART I: SOLVABLE 2-LOCAL SUBGROUPS""; ""1. Introduction""; ""2. The minimal counterexample""; ""3. Odd order groups acting on 2-groups""; ""4. The local subgroups of G""; ""5. The structure of O[sub(2)(M)""; ""6. The case C[sub(R)](B) / 1""; ""7. Proof of Theorem A""; ""PART II: 2-CONSTRAINED 2-LOCAL SUBGROUPS""; ""1. Introduction""; ""2. The automorphism groups of certain 2-groups""; ""3. Theorem B, the GL(3,2) case""; ""4. Theorem B, the A[sub(5)]case""; ""5. Theorems C and D, initial reduction""; ""6. Theorems C and D, the A[sub(5)] case""
""5. The normal four subgroup case""""6. The cyclic case""; ""7. The maximal class case""; ""PART V: CENTRAL INVOLUTIONS WITH NON 2-CONSTRAINED CENTRALIZERS""; ""1. Introduction""; ""2. Initial reductions""; ""3. Theorem A; the wreathed case""; ""4. Preliminary results""; ""5. Maximal elementary abelian 2-subgroups""; ""6. Fusion of involutions""; ""7. Theorem A; the dihedral and quasi-dihedral cases""; ""PART VI: A CHARACTERIZATION OF THE GROUP M[sub(12)]""; ""1. Introduction""; ""2. 2-groups and their automorphism groups""; ""3. Some 2-groups associated with Aut(Z[sub(4)] x Z[sub(4)])"" ""4. Initial reductions""""5. Elimination of the rank 3 case""; ""6. The major reduction""; ""7. The non-dihedral case""; ""8. The noncyclic case""; ""9. The structure of O[sub(2)](M)""; ""10. The structure of S"" |
| Record Nr. | UNINA-9910788616303321 |
Gorenstein Daniel
|
||
| Providence : , : American Mathematical Society, , 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite groups whose 2-subgroups are generated by at most 4 elements / / [by] Daniel Gorenstein and Koichiro Harada
| Finite groups whose 2-subgroups are generated by at most 4 elements / / [by] Daniel Gorenstein and Koichiro Harada |
| Autore | Gorenstein Daniel |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 1974 |
| Descrizione fisica | 1 online resource (473 p.) |
| Disciplina | 512/.2 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Finite groups |
| ISBN | 0-8218-9947-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""TABLE OF CONTENTS""; ""INTRODUCTION""; ""PART I: SOLVABLE 2-LOCAL SUBGROUPS""; ""1. Introduction""; ""2. The minimal counterexample""; ""3. Odd order groups acting on 2-groups""; ""4. The local subgroups of G""; ""5. The structure of O[sub(2)(M)""; ""6. The case C[sub(R)](B) / 1""; ""7. Proof of Theorem A""; ""PART II: 2-CONSTRAINED 2-LOCAL SUBGROUPS""; ""1. Introduction""; ""2. The automorphism groups of certain 2-groups""; ""3. Theorem B, the GL(3,2) case""; ""4. Theorem B, the A[sub(5)]case""; ""5. Theorems C and D, initial reduction""; ""6. Theorems C and D, the A[sub(5)] case""
""5. The normal four subgroup case""""6. The cyclic case""; ""7. The maximal class case""; ""PART V: CENTRAL INVOLUTIONS WITH NON 2-CONSTRAINED CENTRALIZERS""; ""1. Introduction""; ""2. Initial reductions""; ""3. Theorem A; the wreathed case""; ""4. Preliminary results""; ""5. Maximal elementary abelian 2-subgroups""; ""6. Fusion of involutions""; ""7. Theorem A; the dihedral and quasi-dihedral cases""; ""PART VI: A CHARACTERIZATION OF THE GROUP M[sub(12)]""; ""1. Introduction""; ""2. 2-groups and their automorphism groups""; ""3. Some 2-groups associated with Aut(Z[sub(4)] x Z[sub(4)])"" ""4. Initial reductions""""5. Elimination of the rank 3 case""; ""6. The major reduction""; ""7. The non-dihedral case""; ""8. The noncyclic case""; ""9. The structure of O[sub(2)](M)""; ""10. The structure of S"" |
| Record Nr. | UNINA-9910828787003321 |
|
Gorenstein Daniel
|
||
| Providence : , : American Mathematical Society, , 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite simple groups : an introduction to their classification / Daniel Gorenstein
| Finite simple groups : an introduction to their classification / Daniel Gorenstein |
| Autore | Gorenstein, Daniel |
| Pubbl/distr/stampa | New York : Plenum Press, c1982 |
| Descrizione fisica | x, 333 p. ; 24 cm |
| Disciplina | 512.2 |
| Collana | The University Series in Mathematics |
| Soggetto non controllato | Gruppi semplici finiti - Classificazione |
| ISBN | 0-306-40779-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990001262200403321 |
|
Gorenstein, Daniel
|
||
| New York : Plenum Press, c1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite Simple Groups : An Introduction to Their Classification / Daniel Gorenstein
| Finite Simple Groups : An Introduction to Their Classification / Daniel Gorenstein |
| Autore | Gorenstein, Daniel |
| Pubbl/distr/stampa | New York, : Springer, 1982 |
| Descrizione fisica | x, 333 p. : ill. ; 24 cm |
| Soggetto topico |
20-XX - Group theory and generalizations [MSC 2020]
20D06 - Simple groups: alternating groups and groups of Lie type [MSC 2020] 20D05 - Finite simple groups and their classification [MSC 2020] 20D08 - Simple groups: sporadic groups [MSC 2020] |
| Soggetto non controllato |
Boundary Element Methods
Classification Fields Finite Finite Groups Groups History of mathematics Mathematics Proofs Story |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0268508 |
|
Gorenstein, Daniel
|
||
| New York, : Springer, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons
| The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons |
| Autore | Gorenstein Daniel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1983] |
| Descrizione fisica | 1 online resource (742 p.) |
| Disciplina |
510 s
512/.22 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Finite simple groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0686-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Acknowledgements""; ""General Introduction""; ""Part I: Properties of K-groups and Preliminary Lemmas""; ""Chapter 1. Introduction""; ""Â1. Notation""; ""Â2. p-layers""; ""Â3. The known simple groups""; ""Â4. Preliminaries concerning groups of Lie type""; ""Â5. Basic properties of the sporadic groups""; ""Chapter 2. Decorations of the known simple groups""; ""Â6. Schur multipliers and covering groups of the known simple groups""; ""Â7. Automorphisms of the known simple groups""; ""Chapter 3. Local subgroups of the known simple groups""
""Â8. The local structure of classical groups, as seen on their natural modules""""Â9. Outer automorphisms of Chevalley groups""; ""Â10. Sylow structure, p-rank, and 2-local p-rank of the known simple groups""; ""Â11. The permutation action of large elementary abelian p-groups on p-components of K-groups""; ""Â12. p-fusion in the known simple groups""; ""Â13. Parabolic subgroups of Chevalley groups""; ""Â14. Subcomponents and pumpups of the known simple groups""; ""Â15. Action of commuting p-elements on subcomponents of known simple groups"" ""Â16. Splitting primes for groups in Chev (2)""""Â17. Standard subcomponents of groups in Chev (2)""; ""Chapter 4. Balance and signalizers""; ""Â18. L[sub(p)],-balance and related results""; ""Â19. Local and global balance""; ""Â20. Signalizers in the known simple groups""; ""Â21. Signalizer functors""; ""Chapter 5. Generational properties of K-groups""; ""Â22. Generation""; ""Â23. Generation of K-groups""; ""Â24. Strongly p-embedded subgroups and proper k-generated cores in K-groups""; ""Â25. Generation of pumpups of the known simple groups""; ""Â26. Existence of layers"" ""Â27. Balance vs. generation""""Chapter 6. Factorizations""; ""Â28. Factorizations in K-groups""; ""Chapter 7. Miscellaneous general results and lemmas about K-groups""; ""Â29. Groups with self-centralizing elementary abelian subgroups of low rank""; ""Â30. Miscellaneous special lemmas""; ""Â31. p-groups and connectedness""; ""Â32. Miscellaneous general lemmas""; ""Â33. The fundamental property of groups of characteristic 2 type""; ""Appendix""; ""Â34. Elements of order 3 in Chevalley groups of characteristic 2""; ""Part II: The Trichotomy Theorem""; ""Chapter 1. Odd standard form"" ""Â1. Introduction""""Â2. A preliminary lemma""; ""Â3. The p-constrained case""; ""Â4. Maximal p-components""; ""Â5. Partial standard form""; ""Â6. The characteristic of L""; ""Â7. The alternating case""; ""Â8. The sporadic case""; ""Â9. Quasisimplicity""; ""Â10. The embedding of B: field automorphisms""; ""Â11. The embedding of B: splitting and half-splitting primes""; ""Â12. Neighbors""; ""Â13. Coda""; ""Chapter 2. Signalizer functors and weak proper 2-generated p- cores""; ""Â1. Introduction""; ""Â2. Balance""; ""Â3. The p- components of 1[sub(b)]"" ""Â4. Signalizer functors and pre-uniqueness subgroups"" |
| Record Nr. | UNINA-9910480566203321 |
|
Gorenstein Daniel
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1983] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons
| The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons |
| Autore | Gorenstein Daniel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1983] |
| Descrizione fisica | 1 online resource (742 p.) |
| Disciplina |
510 s
512/.22 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Finite simple groups |
| ISBN | 1-4704-0686-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Acknowledgements""; ""General Introduction""; ""Part I: Properties of K-groups and Preliminary Lemmas""; ""Chapter 1. Introduction""; ""Â1. Notation""; ""Â2. p-layers""; ""Â3. The known simple groups""; ""Â4. Preliminaries concerning groups of Lie type""; ""Â5. Basic properties of the sporadic groups""; ""Chapter 2. Decorations of the known simple groups""; ""Â6. Schur multipliers and covering groups of the known simple groups""; ""Â7. Automorphisms of the known simple groups""; ""Chapter 3. Local subgroups of the known simple groups""
""Â8. The local structure of classical groups, as seen on their natural modules""""Â9. Outer automorphisms of Chevalley groups""; ""Â10. Sylow structure, p-rank, and 2-local p-rank of the known simple groups""; ""Â11. The permutation action of large elementary abelian p-groups on p-components of K-groups""; ""Â12. p-fusion in the known simple groups""; ""Â13. Parabolic subgroups of Chevalley groups""; ""Â14. Subcomponents and pumpups of the known simple groups""; ""Â15. Action of commuting p-elements on subcomponents of known simple groups"" ""Â16. Splitting primes for groups in Chev (2)""""Â17. Standard subcomponents of groups in Chev (2)""; ""Chapter 4. Balance and signalizers""; ""Â18. L[sub(p)],-balance and related results""; ""Â19. Local and global balance""; ""Â20. Signalizers in the known simple groups""; ""Â21. Signalizer functors""; ""Chapter 5. Generational properties of K-groups""; ""Â22. Generation""; ""Â23. Generation of K-groups""; ""Â24. Strongly p-embedded subgroups and proper k-generated cores in K-groups""; ""Â25. Generation of pumpups of the known simple groups""; ""Â26. Existence of layers"" ""Â27. Balance vs. generation""""Chapter 6. Factorizations""; ""Â28. Factorizations in K-groups""; ""Chapter 7. Miscellaneous general results and lemmas about K-groups""; ""Â29. Groups with self-centralizing elementary abelian subgroups of low rank""; ""Â30. Miscellaneous special lemmas""; ""Â31. p-groups and connectedness""; ""Â32. Miscellaneous general lemmas""; ""Â33. The fundamental property of groups of characteristic 2 type""; ""Appendix""; ""Â34. Elements of order 3 in Chevalley groups of characteristic 2""; ""Part II: The Trichotomy Theorem""; ""Chapter 1. Odd standard form"" ""Â1. Introduction""""Â2. A preliminary lemma""; ""Â3. The p-constrained case""; ""Â4. Maximal p-components""; ""Â5. Partial standard form""; ""Â6. The characteristic of L""; ""Â7. The alternating case""; ""Â8. The sporadic case""; ""Â9. Quasisimplicity""; ""Â10. The embedding of B: field automorphisms""; ""Â11. The embedding of B: splitting and half-splitting primes""; ""Â12. Neighbors""; ""Â13. Coda""; ""Chapter 2. Signalizer functors and weak proper 2-generated p- cores""; ""Â1. Introduction""; ""Â2. Balance""; ""Â3. The p- components of 1[sub(b)]"" ""Â4. Signalizer functors and pre-uniqueness subgroups"" |
| Record Nr. | UNINA-9910788898803321 |
|
Gorenstein Daniel
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1983] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons
| The local structure of finite groups of characteristic 2 type / / Daniel Gorenstein and Richard Lyons |
| Autore | Gorenstein Daniel |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1983] |
| Descrizione fisica | 1 online resource (742 p.) |
| Disciplina |
510 s
512/.22 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Finite simple groups |
| ISBN | 1-4704-0686-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Acknowledgements""; ""General Introduction""; ""Part I: Properties of K-groups and Preliminary Lemmas""; ""Chapter 1. Introduction""; ""Â1. Notation""; ""Â2. p-layers""; ""Â3. The known simple groups""; ""Â4. Preliminaries concerning groups of Lie type""; ""Â5. Basic properties of the sporadic groups""; ""Chapter 2. Decorations of the known simple groups""; ""Â6. Schur multipliers and covering groups of the known simple groups""; ""Â7. Automorphisms of the known simple groups""; ""Chapter 3. Local subgroups of the known simple groups""
""Â8. The local structure of classical groups, as seen on their natural modules""""Â9. Outer automorphisms of Chevalley groups""; ""Â10. Sylow structure, p-rank, and 2-local p-rank of the known simple groups""; ""Â11. The permutation action of large elementary abelian p-groups on p-components of K-groups""; ""Â12. p-fusion in the known simple groups""; ""Â13. Parabolic subgroups of Chevalley groups""; ""Â14. Subcomponents and pumpups of the known simple groups""; ""Â15. Action of commuting p-elements on subcomponents of known simple groups"" ""Â16. Splitting primes for groups in Chev (2)""""Â17. Standard subcomponents of groups in Chev (2)""; ""Chapter 4. Balance and signalizers""; ""Â18. L[sub(p)],-balance and related results""; ""Â19. Local and global balance""; ""Â20. Signalizers in the known simple groups""; ""Â21. Signalizer functors""; ""Chapter 5. Generational properties of K-groups""; ""Â22. Generation""; ""Â23. Generation of K-groups""; ""Â24. Strongly p-embedded subgroups and proper k-generated cores in K-groups""; ""Â25. Generation of pumpups of the known simple groups""; ""Â26. Existence of layers"" ""Â27. Balance vs. generation""""Chapter 6. Factorizations""; ""Â28. Factorizations in K-groups""; ""Chapter 7. Miscellaneous general results and lemmas about K-groups""; ""Â29. Groups with self-centralizing elementary abelian subgroups of low rank""; ""Â30. Miscellaneous special lemmas""; ""Â31. p-groups and connectedness""; ""Â32. Miscellaneous general lemmas""; ""Â33. The fundamental property of groups of characteristic 2 type""; ""Appendix""; ""Â34. Elements of order 3 in Chevalley groups of characteristic 2""; ""Part II: The Trichotomy Theorem""; ""Chapter 1. Odd standard form"" ""Â1. Introduction""""Â2. A preliminary lemma""; ""Â3. The p-constrained case""; ""Â4. Maximal p-components""; ""Â5. Partial standard form""; ""Â6. The characteristic of L""; ""Â7. The alternating case""; ""Â8. The sporadic case""; ""Â9. Quasisimplicity""; ""Â10. The embedding of B: field automorphisms""; ""Â11. The embedding of B: splitting and half-splitting primes""; ""Â12. Neighbors""; ""Â13. Coda""; ""Chapter 2. Signalizer functors and weak proper 2-generated p- cores""; ""Â1. Introduction""; ""Â2. Balance""; ""Â3. The p- components of 1[sub(b)]"" ""Â4. Signalizer functors and pre-uniqueness subgroups"" |
| Record Nr. | UNINA-9910817126603321 |
|
Gorenstein Daniel
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1983] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Reviews on finite groups / classified by Daniel Gorenstein
| Reviews on finite groups / classified by Daniel Gorenstein |
| Autore | Gorenstein, Daniel |
| Edizione | [Repr. Math. Rev. 1940-1970 v. 1-40] |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, 1974 |
| Descrizione fisica | 2 pt. ; 30 cm. |
| Disciplina | 512.2 |
| Soggetto topico | Finite groups-abstracts |
| ISBN | 0821802012 |
| Classificazione |
AMS 00A15
AMS 05B AMS 05C AMS 13D AMS 20-XX AMS 20B AMS 20C AMS 20D AMS 20G AMS 20H AMS 20J AMS 20K QA171.G642 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001303289707536 |
|
Gorenstein, Daniel
|
||
| Providence, R. I. : American Mathematical Society, 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
The classification of finite simple groups / by Gorenstein
| The classification of finite simple groups / by Gorenstein |
| Autore | Gorenstein, Daniel |
| Pubbl/distr/stampa | New York [etc.] : Plenum Press, 1983 |
| Collana | The University Series in Higher Mathematics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990001262210403321 |
|
Gorenstein, Daniel
|
||
| New York [etc.] : Plenum Press, 1983 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Classification of Finite Simple Groups / Daniel Gorenstein
| The Classification of Finite Simple Groups / Daniel Gorenstein |
| Autore | Gorenstein, Daniel |
| Pubbl/distr/stampa | New York, : Springer |
| Descrizione fisica | volumi ; 24 cm |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0268629 |
|
Gorenstein, Daniel
|
||
| New York, : Springer | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
