Finite groups whose 2-subgroups are generated by at most 4 elements:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1974
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
147 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 464 S. |
| ISBN: | 0821818473 |
Internformat
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| 245 | 1 | 0 | |a Finite groups whose 2-subgroups are generated by at most 4 elements |c Daniel Gorenstein and Koichiro Harada |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1974 | |
| 300 | |a VII, 464 S. | ||
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Datensatz im Suchindex
| _version_ | 1804117341381853184 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION 1
PART I: SOLVABLE 2 LOCAL SUBGROUPS
1. Introduction 9
2. The minimal counterexample 10
3. Odd order groups acting on 2 groups 14
^. The local subgroups of G 29
5. The structure of 02(M) 41
6. The case CR(B) / 1 50
7. Proof of Theorem A 57
PART II: 2 CONSTRAINED 2 LOCAL SUBGROUPS
1. Introduction 68
2. The automorphism groups of certain 2 groups 70
3. Theorem B, the GL(3,2) case 83
•+. Theorem B, the A_ case 103
5. Theorems C and D, initial reduction 105
6. Theorems C and D, the A_ case 113
7. Theorems C and D, the GL(3,2) case 122
PART III: NON 2 CONSTRAINED CENTRALIZERS OF INVOLUTIONS; SOME SPECIAL CASES
1. Introduction 134
2. Theorem A 138
3. The e(8) case 141
h. The A* case 146
6. Some lemmas 162
7. The SLCsq), SU(^,q), Sp(^jq) cases 178
8. The direct product case 187
9. The central product case 200
iii
PART IV: A CHARACTERIZATION OF THE GROUP D^(3)
1. Introduction 219
2. Preliminary lemmas 221
3. The centralizer of a central involution 232
k. The intersection of W and its conjugates 239
5. The normal four subgroup case 247
6. The cyclic case 259
7. The maximal class case 268
PART V: CENTRAL INVOLUTIONS WITH NON 2 CONSTRAINED CENTRALIZERS
1. Introduction 275
2. Initial reductions 276
3. Theorem A; the wreathed case 278
k. Preliminary results 281
5. Maximal elementary abelian 2 subgroups 296
6. Fusion of involutions 307
7. Theorem A; the dihedral and quasi dihedral cases 317
PART VI: A CHARACTERIZATION OF THE GROUP M^
1. Introduction 338
2. 2 groups and their automorphism groups 339
3. Some 2 groups associated with Aut(Z^ x Z, ) 355
k. Initial reductions 369
5. Elimination of the rank 3 case 371
6. The major reduction 376
7. The non dihedral case 401
8. The noncyclic case 414
9. The structure of O2(H) 424
10. The structure of S 447
|
| any_adam_object | 1 |
| author | Gorenstein, Daniel Harada, Kōichirō 1941- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)224999773 (DE-599)BVBBV003052618 |
| dewey-full | 510/.8 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510/.8 512/.2 |
| dewey-search | 510/.8 512/.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV003052618 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:52:52Z |
| institution | BVB |
| isbn | 0821818473 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001912652 |
| oclc_num | 224999773 |
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| physical | VII, 464 S. |
| psigel | TUB-www |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Gorenstein, Daniel Verfasser aut Finite groups whose 2-subgroups are generated by at most 4 elements Daniel Gorenstein and Koichiro Harada Providence, R.I. American Mathematical Society 1974 VII, 464 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 147 Groupes finis Groupes finis ram Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s DE-604 Harada, Kōichirō 1941- Verfasser (DE-588)1018107312 aut American Mathematical Society: Memoirs of the American Mathematical Society 147 (DE-604)BV008000141 147 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001912652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gorenstein, Daniel Harada, Kōichirō 1941- Finite groups whose 2-subgroups are generated by at most 4 elements American Mathematical Society: Memoirs of the American Mathematical Society Groupes finis Groupes finis ram Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4014651-0 |
| title | Finite groups whose 2-subgroups are generated by at most 4 elements |
| title_auth | Finite groups whose 2-subgroups are generated by at most 4 elements |
| title_exact_search | Finite groups whose 2-subgroups are generated by at most 4 elements |
| title_full | Finite groups whose 2-subgroups are generated by at most 4 elements Daniel Gorenstein and Koichiro Harada |
| title_fullStr | Finite groups whose 2-subgroups are generated by at most 4 elements Daniel Gorenstein and Koichiro Harada |
| title_full_unstemmed | Finite groups whose 2-subgroups are generated by at most 4 elements Daniel Gorenstein and Koichiro Harada |
| title_short | Finite groups whose 2-subgroups are generated by at most 4 elements |
| title_sort | finite groups whose 2 subgroups are generated by at most 4 elements |
| topic | Groupes finis Groupes finis ram Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Groupes finis Endliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001912652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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