Sylow theory, formations and fitting classes in locally finite groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u. a.]
World Scient.
1994
|
| Series: | Series in algebra
2 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 304 S. |
| ISBN: | 9810217951 |
Staff View
MARC
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| 245 | 1 | 0 | |a Sylow theory, formations and fitting classes in locally finite groups |c Martyn R. Dixon |
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Record in the Search Index
| _version_ | 1804142003334676480 |
|---|---|
| adam_text | CONTENTS
Preface v
Index of Notation xi
1. Basic concepts 1
1.1 Group theoretical classes and closure operations 1
1.2. Series of subgroups 6
1.3. Radicals and residuals 13
1.4. Local systems 18
1.5. The minimum condition and Cernikov groups 27
1.6. Generalizations of the minimum condition 35
1.7. Some miscellaneous results 46
2. Sylow theory in locally finite groups 53
2.1. Introduction 53
2.2. Elementary results and examples 54
2.3. Conjugacy and the size of |Syl» G 65
2.4. The Asar-Hartley Theorem for a general set of 76
primes
2.5. Groups with min-p 82
2.6 Good Sylow subgroups 93
3. Groups satisfying min-p for all primes p 99
3.1. Sylow theory in groups with min-p for all primes p 99
3.2. Locally soluble groups of finite rank 104
3.3. Some properties of PSL(2, F) 110
3.4. The 2-radicable part of a group with min-p for all p 114
3.5. The structure of groups with min-p for all primes p 125
4. Groups with conjugate Sylow subgroups 141
4.1. Upper jr-separable groups 141
4.2. Groups with the minimum condition on centralizers 144
4.3. The structure of Sylow p-integrated groups 158
4.4. Completely Sylow integrated groups 160
4.5. Metabelian groups with min-n 165
ix
x Contents
5. Sylow bases in locally finite groups 169
5.1. General properties of Sylow bases 169
5.2. Sylow bases in ii-groups 175
5.3. Sylow bases in groups with min-p for all p 181
5.4. Further results on groups with min-p for all p 188
5.5. Co-Hopfian groups 196
6. Formation theory in locally finite groups 205
6.1. A brief historical account 205
6.2. Locally denned formations 207
6.3. The J-normalizers of locally finite groups 216
6.4. JJ-projectors in locally finite groups 230
6.5. Concluding remarks concerning formation theory 245
7. Fitting classes in locally finite groups 251
7.1 A brief historical account 251
7.2. Elementary properties of Fitting classes 252
7.3. Injectors in locally finite groups 257
7.4. Injectors in groups with min-p for all primes p 265
7.5. Conjugacy conditions for injectors in £-groups 272
7.6. Closing remarks 280
Bibliography 283
Index 299
|
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| indexdate | 2024-07-09T22:24:51Z |
| institution | BVB |
| isbn | 9810217951 |
| language | English |
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| physical | XIII, 304 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | World Scient. |
| record_format | marc |
| series | Series in algebra |
| series2 | Series in algebra |
| spelling | Dixon, Martyn R. Verfasser aut Sylow theory, formations and fitting classes in locally finite groups Martyn R. Dixon Singapore [u. a.] World Scient. 1994 XIII, 304 S. txt rdacontent n rdamedia nc rdacarrier Series in algebra 2 Series in algebra 2 (DE-604)BV010096634 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641578&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dixon, Martyn R. Sylow theory, formations and fitting classes in locally finite groups Series in algebra |
| title | Sylow theory, formations and fitting classes in locally finite groups |
| title_auth | Sylow theory, formations and fitting classes in locally finite groups |
| title_exact_search | Sylow theory, formations and fitting classes in locally finite groups |
| title_full | Sylow theory, formations and fitting classes in locally finite groups Martyn R. Dixon |
| title_fullStr | Sylow theory, formations and fitting classes in locally finite groups Martyn R. Dixon |
| title_full_unstemmed | Sylow theory, formations and fitting classes in locally finite groups Martyn R. Dixon |
| title_short | Sylow theory, formations and fitting classes in locally finite groups |
| title_sort | sylow theory formations and fitting classes in locally finite groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641578&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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