Theory of finite simple groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Series: | New mathematical monographs
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 662 S. graph. Darst. 1 CD-ROM |
| ISBN: | 0521866251 9780521866255 |
Staff View
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Record in the Search Index
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| adam_text | THEORY OF FINITE SIMPLE GROUPS GERHARD O. MICHLER INSTITUTE OF
EXPERIMENTAL MATHEMATICS UNIVERSITY OF DUISBURG-ESSEN AND CORNELL
UNIVERSITY CAMBRIDGE UNIVERSITY PRESS CONTENTS ACKNOWLEDGEMENTS PAGE XI
LIST OF SYMBOLS - XII INTRODUCTION 1 1 PREREQUISITES FROM GROUP THEORY 8
1.1 PRESENTATIONS OF GROUPS 9 1.2 GENERALIZED QUATERNION GROUPS 12 1.3
2-GROUPS WITHOUT NON-CYCLIC ABELIAN CHARACTERISTIC SUBGROUPS 15 1.4
TRANSFER AND FUSION OF ELEMENTS 25 1.5 COPRIME GROUP ACTIONS . 34 1.6
SIMPLE GROUPS WITH DIHEDRAL OR SEMI-DIHEDRAL SYLOW 2-SUBGROUPS 38 1.7
SIMPLE GROUPS WITH STRONGLY EMBEDDED SUBGROUPS 40 2 GROUP
REPRESENTATIONS AND CHARACTER THEORY 42 2.1 ALGEBRAS, MODULES AND
REPRESENTATIONS 43 2.2 CONJUGACY CLASSES OF FINITE GROUPS 52 2.3
CHARACTERS OF FINITE GROUPS 55 2.4 CHARACTERS AND ALGEBRAIC INTEGERS 64
2.5 TENSOR PRODUCTS 68 2.6 INDUCTION AND RESTRICTION 74 2.7 FROBENIUS
GROUPS AND EXCEPTIONAL CHARACTERS 82 2.8 BRAUER S CHARACTERIZATION OF
CHARACTERS 90 2.9 PROJECTIVE REPRESENTATIONS AND CENTRAL EXTENSIONS 97 3
MODULAR REPRESENTATION THEORY 110 3.1 EXISTENCE OF SPLITTING P-MODULAR
SYSTEMS 112 3.2 INDECOMPOSABLE MODULES 123 3.3 SEMI-PERFECT RINGS 128
3.4 GROUP LATTICES AND HELLER MODULES 137 3.5 RELATIVE-PROJECTIVE
MODULES AND HOMOMORPHISMS 144 3.6 BLOCKS OF FINITE GROUPS 153 3.7 DEFECT
GROUPS 160 3.8 BRAUER S FIRST MAIN THEOREM 163 3.9 SUPPORT AND KERNEL OF
A BLOCK IDEMPOTENT 170 3.10 VERTICES AND SOURCES 174 3.11 MODULAR
CHARACTERS OF FINITE GROUPS 181 3.12 BLOCKS OF DEFECT ZERO 187 3.13
GREEN CORRESPONDENCE 189 VIII CONTENTS 3.14 BLOCKS AND NORMAL SUBGROUPS
200 3.15 BLOCKS WITH NORMAL DEFECT GROUPS 206 3.16 BRAUER S SECOND AND
THIRD MAIN THEOREMS 212 3.17 BLOCKS OF DEFECT ONE 222 GROUP ORDER
FORMULAS AND STRUCTURE THEOREM 242 4.1 SUZUKI S GROUP ORDER FORMULA 243
4.2 THOMPSON S GROUP ORDER FORMULA 246 4.3 GROUPS WITH A UNIQUE
CONJUGACY CLASS OF INVOLUTIONS 248 4.4 BRAUER S GROUP ORDER FORMULA 256
4.5 A THEOREM OF G. FROBENIUS 259 4.6 BRAUER-SUZUKI THEOREM 260 4.7
GLAUBERMAN S Z*-THEOREM 266 4.8 STRUCTURE THEOREM 269 PERMUTATION
REPRESENTATIONS 277 5.1 PERMUTATION GROUPS 278 5.2 ORBITS, STABILIZERS
AND GROUP ORDER 281 5.3 CONJUGACY CLASSES OF PERMUTATION GROUPS 289 5.4
ENDOMORPHISM RINGS OF PERMUTATION MODULES 295 5.5 INTERSECTION ALGEBRAS
301 5.6 CHARACTER FORMULA OF MICHLER AND WELLER 307 5.7 ALGORITHM FOR
COMPUTING CHARACTER VALUES 314 5.8 COMPLETION OF CONCRETE CHARACTER
TABLE CALCULATIONS 316 CONCRETE CHARACTER TABLES OF MATRIX GROUPS 320
6.1 NORTON S IRREDUCIBILITY CRITERION 320 6.2 FROM MATRIX GROUPS TO
PERMUTATION GROUPS 324 6.3 CONJUGACY CLASSES OF MATRIX GROUPS 326 6.4
EXAMPLE OF A CONCRETE CHARACTER TABLE CALCULATION 328 METHODS FOR
CONSTRUCTING FINITE SIMPLE GROUPS 333 7.1 FREE PRODUCTS WITH AN
AMALGAMATED SUBGROUP 334 7.2 IRREDUCIBLE REPRESENTATIONS OF FREE
PRODUCTS WITH AMALGAMATED SUBGROUPS 341 7.3 KRATZER S ALGORITHM
COMPUTING COMPATIBLE CHARACTERS 348 7.4 MICHLER S ALGORITHM CONSTRUCTING
SIMPLE GROUPS FROM GIVEN CENTRALIZERS 354 7.5 UNIQUENESS CRITERION 364
FINITE SIMPLE GROUPS WITH PROPER SATELLITES 376 8.1 MATHIEU GROUPS MN
AND MI 2 377 8.2 MATHIEU GROUPS M 2 2, M23 AND M 2 4 388 8.3 THE
SATELLITES OF M 2 4 397 CONTENTS IX 8.4 GENERATING MATRICES OF THE HELD
GROUP HE IN GL5I(LL) 406 8.5 JANKO S SPORADIC GROUPS J 2 AND J3 409 8.6
SIMPLE SATELLITES OF THE ALTERNATING GROUPS 418 9 JANKO GROUP JI 433 9.1
STRUCTURE OF THE GIVEN CENTRALIZER 433 9.2 CHARACTER TABLE OF GROUPS OF
JI-TYPE 435 9.3 EXISTENCE PROOF 447 9.4 UNIQUENESS PROOF 452 10
HIGMAN-SIMS GROUP HS 455 10.1 STRUCTURE OF THE GIVEN CENTRALIZER 455
10.2 FUSION 457 10.3 EXISTENCE PROOF OF HS INSIDE GL 22 (11) 473 10.4
UNIQUENESS OF HS 476 10.5 A PRESENTATION FOR AUT(HS) - 478 10.6
REPRESENTATIVES OF CONJUGACY CLASSES 480 10.7 CHARACTER TABLES 483 11
HARADA GROUP HA 487 11.1 THE CENTRALIZER OF A 2-CENTRAL INVOLUTION 487
11.2 THE EXISTENCE PROOF 491 11.3 UNIQUENESS 497 11.4 REPRESENTATIVES OF
CONJUGACY CLASSES 525 11.5 CHARACTER TABLES 530 11.6 GENERATING MATRICES
A, B, C * GL 133 (19) OF 0 546 12 THOMPSON GROUP TH 554 12.1 THE
CENTRALIZER OF A 2-CENTRAL INVOLUTION 555 12.2 CONJUGACY CLASSES OF
ELEMENTS OF EVEN ORDER 557 12.3 EXISTENCE PROOF OF TH INSIDE GI/ 2
48(11) 561 12.4 DETERMINATION OF THE 3-SINGULAR CONJUGACY CLASSES 571
12.5 THE 5-, 7- AND 13-SINGULAR CONJUGACY CLASSES 598 12.6 GROUP ORDER
607 12.7 UNIQUENESS PROOF AND CONCRETE CHARACTER TABLE 611 12.8
REPRESENTATIVES OF CONJUGACY CLASSES 616 12.9 CHARACTER TABLES 622
12.10PARTIAL CHARACTER TABLE OF MATRIX GROUP 0 641 REFERENCES 645 INDEX
656
|
| adam_txt |
THEORY OF FINITE SIMPLE GROUPS GERHARD O. MICHLER INSTITUTE OF
EXPERIMENTAL MATHEMATICS UNIVERSITY OF DUISBURG-ESSEN AND CORNELL
UNIVERSITY CAMBRIDGE UNIVERSITY PRESS CONTENTS ACKNOWLEDGEMENTS PAGE XI
LIST OF SYMBOLS - XII INTRODUCTION 1 1 PREREQUISITES FROM GROUP THEORY 8
1.1 PRESENTATIONS OF GROUPS 9 1.2 GENERALIZED QUATERNION GROUPS 12 1.3
2-GROUPS WITHOUT NON-CYCLIC ABELIAN CHARACTERISTIC SUBGROUPS 15 1.4
TRANSFER AND FUSION OF ELEMENTS 25 1.5 COPRIME GROUP ACTIONS . 34 1.6
SIMPLE GROUPS WITH DIHEDRAL OR SEMI-DIHEDRAL SYLOW 2-SUBGROUPS 38 1.7
SIMPLE GROUPS WITH STRONGLY EMBEDDED SUBGROUPS 40 2 GROUP
REPRESENTATIONS AND CHARACTER THEORY 42 2.1 ALGEBRAS, MODULES AND
REPRESENTATIONS 43 2.2 CONJUGACY CLASSES OF FINITE GROUPS 52 2.3
CHARACTERS OF FINITE GROUPS 55 2.4 CHARACTERS AND ALGEBRAIC INTEGERS 64
2.5 TENSOR PRODUCTS 68 2.6 INDUCTION AND RESTRICTION 74 2.7 FROBENIUS
GROUPS AND EXCEPTIONAL CHARACTERS 82 2.8 BRAUER'S CHARACTERIZATION OF
CHARACTERS 90 2.9 PROJECTIVE REPRESENTATIONS AND CENTRAL EXTENSIONS 97 3
MODULAR REPRESENTATION THEORY 110 3.1 EXISTENCE OF SPLITTING P-MODULAR
SYSTEMS 112 3.2 INDECOMPOSABLE MODULES 123 3.3 SEMI-PERFECT RINGS 128
3.4 GROUP LATTICES AND HELLER MODULES 137 3.5 RELATIVE-PROJECTIVE
MODULES AND HOMOMORPHISMS 144 3.6 BLOCKS OF FINITE GROUPS 153 3.7 DEFECT
GROUPS 160 3.8 BRAUER'S FIRST MAIN THEOREM 163 3.9 SUPPORT AND KERNEL OF
A BLOCK IDEMPOTENT 170 3.10 VERTICES AND SOURCES 174 3.11 MODULAR
CHARACTERS OF FINITE GROUPS 181 3.12 BLOCKS OF DEFECT ZERO 187 3.13
GREEN CORRESPONDENCE 189 VIII CONTENTS 3.14 BLOCKS AND NORMAL SUBGROUPS
200 3.15 BLOCKS WITH NORMAL DEFECT GROUPS 206 3.16 BRAUER'S SECOND AND
THIRD MAIN THEOREMS 212 3.17 BLOCKS OF DEFECT ONE 222 GROUP ORDER
FORMULAS AND STRUCTURE THEOREM 242 4.1 SUZUKI'S GROUP ORDER FORMULA 243
4.2 THOMPSON'S GROUP ORDER FORMULA 246 4.3 GROUPS WITH A UNIQUE
CONJUGACY CLASS OF INVOLUTIONS 248 4.4 BRAUER'S GROUP ORDER FORMULA 256
4.5 A THEOREM OF G. FROBENIUS 259 4.6 BRAUER-SUZUKI THEOREM 260 4.7
GLAUBERMAN'S Z*-THEOREM 266 4.8 STRUCTURE THEOREM 269 PERMUTATION
REPRESENTATIONS 277 5.1 PERMUTATION GROUPS 278 5.2 ORBITS, STABILIZERS
AND GROUP ORDER 281 5.3 CONJUGACY CLASSES OF PERMUTATION GROUPS 289 5.4
ENDOMORPHISM RINGS OF PERMUTATION MODULES 295 5.5 INTERSECTION ALGEBRAS
301 5.6 CHARACTER FORMULA OF MICHLER AND WELLER 307 5.7 ALGORITHM FOR
COMPUTING CHARACTER VALUES 314 5.8 COMPLETION OF CONCRETE CHARACTER
TABLE CALCULATIONS 316 CONCRETE CHARACTER TABLES OF MATRIX GROUPS 320
6.1 NORTON'S IRREDUCIBILITY CRITERION 320 6.2 FROM MATRIX GROUPS TO
PERMUTATION GROUPS 324 6.3 CONJUGACY CLASSES OF MATRIX GROUPS 326 6.4
EXAMPLE OF A CONCRETE CHARACTER TABLE CALCULATION 328 METHODS FOR
CONSTRUCTING FINITE SIMPLE GROUPS 333 7.1 FREE PRODUCTS WITH AN
AMALGAMATED SUBGROUP 334 7.2 IRREDUCIBLE REPRESENTATIONS OF FREE
PRODUCTS WITH AMALGAMATED SUBGROUPS 341 7.3 KRATZER'S ALGORITHM
COMPUTING COMPATIBLE CHARACTERS 348 7.4 MICHLER'S ALGORITHM CONSTRUCTING
SIMPLE GROUPS FROM GIVEN CENTRALIZERS 354 7.5 UNIQUENESS CRITERION 364
FINITE SIMPLE GROUPS WITH PROPER SATELLITES 376 8.1 MATHIEU GROUPS MN
AND MI 2 377 8.2 MATHIEU GROUPS M 2 2, M23 AND M 2 4 388 8.3 THE
SATELLITES OF M 2 4 397 CONTENTS IX 8.4 GENERATING MATRICES OF THE HELD
GROUP HE IN GL5I(LL) 406 8.5 JANKO'S SPORADIC GROUPS J 2 AND J3 409 8.6
SIMPLE SATELLITES OF THE ALTERNATING GROUPS 418 9 JANKO GROUP JI 433 9.1
STRUCTURE OF THE GIVEN CENTRALIZER 433 9.2 CHARACTER TABLE OF GROUPS OF
JI-TYPE 435 9.3 EXISTENCE PROOF 447 9.4 UNIQUENESS PROOF 452 10
HIGMAN-SIMS GROUP HS 455 10.1 STRUCTURE OF THE GIVEN CENTRALIZER 455
10.2 FUSION ' 457 10.3 EXISTENCE PROOF OF HS INSIDE GL 22 (11) 473 10.4
UNIQUENESS OF HS 476 10.5 A PRESENTATION FOR AUT(HS) - 478 10.6
REPRESENTATIVES OF CONJUGACY CLASSES 480 10.7 CHARACTER TABLES 483 11
HARADA GROUP HA 487 11.1 THE CENTRALIZER OF A 2-CENTRAL INVOLUTION 487
11.2 THE EXISTENCE PROOF 491 11.3 UNIQUENESS 497 11.4 REPRESENTATIVES OF
CONJUGACY CLASSES 525 11.5 CHARACTER TABLES 530 11.6 GENERATING MATRICES
A, B, C * GL 133 (19) OF 0 546 12 THOMPSON GROUP TH 554 12.1 THE
CENTRALIZER OF A 2-CENTRAL INVOLUTION 555 12.2 CONJUGACY CLASSES OF
ELEMENTS OF EVEN ORDER 557 12.3 EXISTENCE PROOF OF TH INSIDE GI/ 2
48(11) 561 12.4 DETERMINATION OF THE 3-SINGULAR CONJUGACY CLASSES 571
12.5 THE 5-, 7- AND 13-SINGULAR CONJUGACY CLASSES 598 12.6 GROUP ORDER
607 12.7 UNIQUENESS PROOF AND CONCRETE CHARACTER TABLE 611 12.8
REPRESENTATIVES OF CONJUGACY CLASSES 616 12.9 CHARACTER TABLES 622
12.10PARTIAL CHARACTER TABLE OF MATRIX GROUP 0 641 REFERENCES 645 INDEX
656 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:56:30Z |
| indexdate | 2024-07-09T20:45:35Z |
| institution | BVB |
| isbn | 0521866251 9780521866255 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015040570 |
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| owner_facet | DE-19 DE-BY-UBM DE-20 DE-11 DE-188 |
| physical | IX, 662 S. graph. Darst. 1 CD-ROM |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Michler, Gerhard O. 1938- Verfasser (DE-588)117712760 aut Theory of finite simple groups Gerhard O. Michler 1. publ. Cambridge Cambridge Univ. Press 2006 IX, 662 S. graph. Darst. 1 CD-ROM txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 8 Finite simple groups Endliche einfache Gruppe (DE-588)4123136-3 gnd rswk-swf Endliche einfache Gruppe (DE-588)4123136-3 s DE-604 New mathematical monographs 8 (DE-604)BV035420183 8 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015040570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michler, Gerhard O. 1938- Theory of finite simple groups New mathematical monographs Finite simple groups Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| subject_GND | (DE-588)4123136-3 |
| title | Theory of finite simple groups |
| title_auth | Theory of finite simple groups |
| title_exact_search | Theory of finite simple groups |
| title_exact_search_txtP | Theory of finite simple groups |
| title_full | Theory of finite simple groups Gerhard O. Michler |
| title_fullStr | Theory of finite simple groups Gerhard O. Michler |
| title_full_unstemmed | Theory of finite simple groups Gerhard O. Michler |
| title_short | Theory of finite simple groups |
| title_sort | theory of finite simple groups |
| topic | Finite simple groups Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| topic_facet | Finite simple groups Endliche einfache Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015040570&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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