Finite groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS Chelsea Publ.
2007
|
| Edition: | 2. ed., reprinted |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 519 S. |
| ISBN: | 9780821843420 082184342 7 |
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MARC
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Record in the Search Index
| _version_ | 1804138535521878016 |
|---|---|
| adam_text | CONTENTS
Preface
xi
PART I: METHODS
CHAPTER
1.
PRELIMINARIES
3
1.
Notation and Terminology
4
2.
Assumed Results
5
3.
Related Elementary Results
9
CHAPTER
2.
SOME BASIC TOPICS
15
1. Characteristic Subgroups
15
2.
Elementary Properties of Commutators
18
3. Nilpotent
Groups
21
4.
Solvable Groups
23
5.
Semidirect and Central Products
25
6.
Automorphisms as Linear Transformations
29
7.
Transitive and Doubly Transitive Permutation Groups
33
8.
The Two-Dimensional Linear and
Projective
Groups
39
CHAPTER
3.
REPRESENTATIONS OF GROUPS
58
1.
Basic Concepts
58
2.
Representations of Abelian Groups
64
3.
Complete Reducibility
66
4.
Clifford s Theorem
70
vii
viii Contents
5. G-Homomorphisms 75
6.
Irreducible Representations and Group Algebras
82
7.
Representations of Direct and Central Products
99
8.
/»-Stable Representations
102
CHAPTER
4.
CHARACTER THEORY
112
1.
Basic Properties
112
2.
The Orthogonality Relations
119
3.
Some Applications
130
4.
Induced Characters and Trivial Intersection Sets
134
5.
Frobenius Groups
140
6.
Coherence
148
7.
Brauer s Characterization of Characters
160
CHAPTER
5.
GROUPS OF PRIME POWER ORDER
172
1.
The Frattini Subgroup
173
2.
/» -Automorphisms of Abelian /»-Groups
175
3.
ρ
-Automorphisms of /»-Groups
178
4.
/»-groups of Small Depth
188
5.
Extra-special /»-Groups
203
6.
The Associated Lie Ring
208
CHAPTER
6.
SOLVABLE AND 7T-SOLVABLE GROUPS
217
1.
The Fitting and Frattini Subgroups
217
2.
The Schur-Zassenhaus Theorem
220
3.
Tr-Separable and ^-Solvable groups
226
4.
Solvable Groups
231
5.
¿»-Stability in /»-Solvable Groups
234
CHAPTER
7.
FUSION, TRANSFER, AND /»-FACTOR GROUPS
238
1.
Local Fusion
238
2.
Alperin s Theorem
240
3.
Transfer and the Focal Subgroup
245
4.
Theorems of Burnside, Frobenius, and
Grün 251
5.
Weak Closure and /»-Normality
255
6.
Elementary Applications
257
7.
Groups with Dihedral Sylow 2-Subgroups
260
CHAPTER
8.
/»-CONSTRAINED AND /»-STABLE GROUPS
267
1.
/»-Constraint and /»-Stability
268
2.
Glauberman s Theorem
270
Contents ix
3. The Glauberman-Thompson Normal p-Complement Theorem 280
4.
Groups with Subgroups of Glauberman Type
281
5.
The Thompson Transitivity Theorem
288
6.
The Maximal Subgroup Theorem
294
CHAPTER
9.
GROUPS OF EVEN ORDER
300
1.
Elementary Properties of Involutions
301
2.
The Feit-Suzuki-Thompson Theorems
306
3.
Two Applications
310
4.
Group Order Formulas
315
PART II: APPLICATIONS
CHAPTER
10.
FIXED-POINT-FREE AUTOMORPHISMS
333
1.
Elementary Properties
333
2.
Fixed-Point-Free Automorphisms of Prime Order
337
3.
Frobenius Groups and Groups with
Nilpotent
Maximal Subgroups
339
4.
Fixed-Point-Free Automorphisms of Order
4 340
5.
Fixed-Point-Free Four-Groups of Automorphisms
345
CHAPTER
11.
THE HALL-HIGMAN THEOREM
358
1.
Statement and Initial Reductions
359
2.
The Extra-Special Case
363
CHAPTER
12.
GROUPS WITH GENERALIZED QUATERNION
SYLOW 2-SUBGROUPS
373
CHAPTER
13.
ZASSENHAUS GROUPS
378
1.
Elementary Properties
379
2.
Feit s Theorem
383
3.
Classification of Certain Zassenhaus Groups
388
CHAPTER
14.
GROUPS IN WHICH CENTRALIZERS ARE NILPOTENT
399
1.
Basic Properties of CW-Groups
400
2.
CTV-Groups of Odd Order
405
3.
Solvability of CW-Groups of Odd Order
409
4.
CTV-Groups with Abelian Sylow 2-Subgroups
415
χ
Contents
CHAPTER
15.
GROUPS WITH SELF-CENTRALIZING SYLOW 2-SUB¬
GROUPS OF ORDER
4 417
1.
Some Properties of L2(q)
418
2.
Statement of the Theorem and Initial Reduction
420
3.
The Structure of the Centralizer of an Involution
423
4.
The Brauer-Suzuki-Wall Theorem
433
PART III: GENERAL CLASSIFICATION PROBLEMS
CHAPTER
16.
SIMPLE GROUPS OF LOW RANK
443
1.
General Methods and Objectives
445
2.
Groups of Odd Order
450
3.
Groups with Dihedral Sylovv 2-Subgroups
462
4.
C-Groups
465
5.
W-Groups
473
6.
Groups with Abelian Sylow 2-Subgroups
480
7.
Other Classification Theorems
486
CHAPTER
17.
THE KNOWN SIMPLE GROUPS
489
The Families of Known Simple Groups
489
Bibliography
497
List of Symbols
511
Index
515
|
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| author_facet | Gorenstein, Daniel |
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| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)180751292 (DE-599)BSZ282664866 |
| discipline | Mathematik |
| edition | 2. ed., reprinted |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:29:44Z |
| institution | BVB |
| isbn | 9780821843420 082184342 7 |
| language | English |
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| physical | XVII, 519 S. |
| publishDate | 2007 |
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| publisher | AMS Chelsea Publ. |
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| spelling | Gorenstein, Daniel Verfasser aut Finite groups Daniel Gorenstein 2. ed., reprinted Providence, RI AMS Chelsea Publ. 2007 XVII, 519 S. txt rdacontent n rdamedia nc rdacarrier Finite groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017060461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gorenstein, Daniel Finite groups Finite groups Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4014651-0 |
| title | Finite groups |
| title_auth | Finite groups |
| title_exact_search | Finite groups |
| title_full | Finite groups Daniel Gorenstein |
| title_fullStr | Finite groups Daniel Gorenstein |
| title_full_unstemmed | Finite groups Daniel Gorenstein |
| title_short | Finite groups |
| title_sort | finite groups |
| topic | Finite groups Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Finite groups Endliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017060461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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