Symmetric generation of groups: with applications to many of the sporadic finite simple groups
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
111 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xiv, 317 S. graph. Darst. 24 cm |
| ISBN: | 052185721X 9780521857215 |
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| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS SYMMETRIC GENERATION OF
GROUPS WITH APPLICATIONS TO MANY OF THE SPORADIC FINITE SIMPLE GROUPS
ROBERT T. CURTIS UNIVERSITY OF BIRMINGHAM, UK CAMBRIDGE UNIVERSITY PRESS
CONTENTS PREFACE ACKNOWLEDGEMENTS XIII I MOTIVATION 1 INTRODUCTION TO
PART I 2 1 THE MATHIEU GROUP M 12 3 1.1 THE COMBINATORIAL APPROACH 3 1.2
THE REGULAR DODECAHEDRON 7 1.3 THE ALGEBRAIC APPROACH 9 1.4 INDEPENDENT
PROOFS 10 2 THE MATHIEU GROUP M 24 15 2.1 THE COMBINATORIAL APPROACH 15
2.2 THE KLEIN MAP 18 2.3 THE ALGEBRAIC APPROACH , 25 2.4 INDEPENDENT
PROOFS 26 CONCLUSIONS TO PART I 40 II INVOLUTORY SYMMETRIC GENERATORS 43
3 THE (INVOLUTORY) PROGENITOR 45 3.1 FREE PRODUCTS OF CYCLIC GROUPS OF
ORDER 2 45 3.2 SEMI-DIRECT PRODUCTS AND THE PROGENITOR P 46 3.3 THE
CAYLEY GRAPH OF P OVER T V 50 3.4 THE REGULAR GRAPH PRESERVED BY P 54
3.5 HOMOMORPHIC IMAGES OF P 54 3.6 THE LEMMA 58 3.7 FURTHER PROPERTIES
OF THE PROGENITOR 59 3.8 COXETER DIAGRAMS AND Y-DIAGRAMS 62 VIII
CONTENTS 3.9 INTRODUCTION TO MAGMA AND GAP 64 3.10 ALGORITHM FOR DOUBLE
COSET ENUMERATION 66 3.11 SYSTEMATIC APPROACH 74 4 CLASSICAL EXAMPLES 89
4.1 THE GROUP PGL 2 (7) 89 4.2 EXCEPTIONAL BEHAVIOUR OF S N 97 4.3 THE
11-POINT BIPLANE AND PGL 2 (11) 116 4.4 THE GROUP OF THE 28 BITANGENTS
121 5 SPORADIC SIMPLE GROUPS 127 5.1 THE MATHIEU GROUP M 22 127 5.2 THE
JANKO GROUP J : 137 5.3 THE HIGMAN-SIMS GROUP 147 5.4 THE HALL-JANKO
GROUP AND THE SUZUKI CHAIN 161 5.5 THE MATHIEU GROUPS M 12 AND M 24 173
5.6 THE JANKO GROUP J 3 174 5.7 THE MATHIEU GROUP M 24 AS CONTROL
SUBGROUP 177 5.8 THE FISCHER GROUPS 226 5.9 TRANSITIVE EXTENSIONS AND
THE O NAN GROUP 233 5.10 SYMMETRIC REPRESENTATION OF GROUPS 235 5.11
APPENDIX TO CHAPTER 5 238 III NON-INVOLUTORY SYMMETRIC GENERATORS 247 6
THE (NON-INVOLUTORY) PROGENITOR 249 6.1 MONOMIAL AUTOMORPHISMS 249 6.2
MONOMIAL REPRESENTATIONS . 250 6.3 MONOMIAL ACTION OF A CONTROL SUBGROUP
256 7 IMAGES OF THE PROGENITORS IN CHAPTER 6 263 7.1 THE MATHIEU GROUP M
U 263 7.2 THE MATHIEU GROUP M 23 267 7.3 THE MATHIEU GROUP M 24 . 271
7.4 FACTORING OUT A CLASSICAL RELATOR 273 7.5 THE SUZUKI CHAIN AND THE
CONWAY GROUP 288 7.6 SYSTEMATIC APPROACH 292 7.7 TABULATED RESULTS 301
7.8 SOME SPORADIC GROUPS 308 REFERENCES 309 INDEX 315
|
| adam_txt |
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS SYMMETRIC GENERATION OF
GROUPS WITH APPLICATIONS TO MANY OF THE SPORADIC FINITE SIMPLE GROUPS
ROBERT T. CURTIS UNIVERSITY OF BIRMINGHAM, UK CAMBRIDGE UNIVERSITY PRESS
CONTENTS PREFACE ACKNOWLEDGEMENTS XIII I MOTIVATION 1 INTRODUCTION TO
PART I 2 1 THE MATHIEU GROUP M 12 3 1.1 THE COMBINATORIAL APPROACH 3 1.2
THE REGULAR DODECAHEDRON 7 1.3 THE ALGEBRAIC APPROACH 9 1.4 INDEPENDENT
PROOFS 10 2 THE MATHIEU GROUP M 24 15 2.1 THE'COMBINATORIAL APPROACH 15
2.2 THE KLEIN MAP 18 2.3 THE ALGEBRAIC APPROACH , 25 2.4 INDEPENDENT
PROOFS 26 CONCLUSIONS TO PART I 40 II INVOLUTORY SYMMETRIC GENERATORS 43
3 THE (INVOLUTORY) PROGENITOR 45 3.1 FREE PRODUCTS OF CYCLIC GROUPS OF
ORDER 2 45 3.2 SEMI-DIRECT PRODUCTS AND THE PROGENITOR P 46 3.3 THE
CAYLEY GRAPH OF P OVER T V 50 3.4 THE REGULAR GRAPH PRESERVED BY P 54
3.5 HOMOMORPHIC IMAGES OF P 54 3.6 THE LEMMA 58 3.7 FURTHER PROPERTIES
OF THE PROGENITOR 59 3.8 COXETER DIAGRAMS AND Y-DIAGRAMS 62 VIII
CONTENTS 3.9 INTRODUCTION TO MAGMA AND GAP 64 3.10 ALGORITHM FOR DOUBLE
COSET ENUMERATION 66 3.11 SYSTEMATIC APPROACH 74 4 CLASSICAL EXAMPLES 89
4.1 THE GROUP PGL 2 (7) 89 4.2 EXCEPTIONAL BEHAVIOUR OF S N 97 4.3 THE
11-POINT BIPLANE AND PGL 2 (11) 116 4.4 THE GROUP OF THE 28 BITANGENTS
121 5 SPORADIC SIMPLE GROUPS 127 5.1 THE MATHIEU GROUP M 22 127 5.2 THE
JANKO GROUP J : 137 5.3 THE HIGMAN-SIMS GROUP 147 5.4 THE HALL-JANKO
GROUP AND THE SUZUKI CHAIN 161 5.5 THE MATHIEU GROUPS M 12 AND M 24 173
5.6 THE JANKO GROUP J 3 174 5.7 THE MATHIEU GROUP M 24 AS CONTROL
SUBGROUP 177 5.8 THE FISCHER GROUPS 226 5.9 TRANSITIVE EXTENSIONS AND
THE O'NAN GROUP 233 5.10 SYMMETRIC REPRESENTATION OF GROUPS 235 5.11
APPENDIX TO CHAPTER 5 238 III NON-INVOLUTORY SYMMETRIC GENERATORS 247 6
THE (NON-INVOLUTORY) PROGENITOR 249 6.1 MONOMIAL AUTOMORPHISMS 249 6.2
MONOMIAL REPRESENTATIONS . 250 6.3 MONOMIAL ACTION OF A CONTROL SUBGROUP
256 7 IMAGES OF THE PROGENITORS IN CHAPTER 6 263 7.1 THE MATHIEU GROUP M
U 263 7.2 THE MATHIEU GROUP M 23 267 7.3 THE MATHIEU GROUP M 24 . 271
7.4 FACTORING OUT A 'CLASSICAL' RELATOR 273 7.5 THE SUZUKI CHAIN AND THE
CONWAY GROUP 288 7.6 SYSTEMATIC APPROACH 292 7.7 TABULATED RESULTS 301
7.8 SOME SPORADIC GROUPS 308 REFERENCES 309 INDEX 315 |
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| dewey-full | 512.2 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
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| index_date | 2024-07-02T22:06:53Z |
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| isbn | 052185721X 9780521857215 |
| language | English |
| lccn | 2007298511 |
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| physical | xiv, 317 S. graph. Darst. 24 cm |
| publishDate | 2007 |
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| publisher | Cambridge Univ. Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Curtis, Robert Verfasser aut Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis 1. publ. Cambridge Cambridge Univ. Press 2007 xiv, 317 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 111 Includes bibliographical references and index Groepentheorie gtt Sporadic groups (Mathematics) Finite simple groups Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Sporadische Gruppe (DE-588)4389412-4 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 s Sporadische Gruppe (DE-588)4389412-4 s DE-604 Encyclopedia of mathematics and its applications 111 (DE-604)BV000903719 111 http://www.loc.gov/catdir/enhancements/fy0803/2007298511-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0803/2007298511-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0803/2007298511-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016748608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Curtis, Robert Symmetric generation of groups with applications to many of the sporadic finite simple groups Encyclopedia of mathematics and its applications Groepentheorie gtt Sporadic groups (Mathematics) Finite simple groups Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd Sporadische Gruppe (DE-588)4389412-4 gnd |
| subject_GND | (DE-588)4184204-2 (DE-588)4389412-4 |
| title | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_auth | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_exact_search | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_exact_search_txtP | Symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_full | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_fullStr | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_full_unstemmed | Symmetric generation of groups with applications to many of the sporadic finite simple groups Robert T. Curtis |
| title_short | Symmetric generation of groups |
| title_sort | symmetric generation of groups with applications to many of the sporadic finite simple groups |
| title_sub | with applications to many of the sporadic finite simple groups |
| topic | Groepentheorie gtt Sporadic groups (Mathematics) Finite simple groups Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd Sporadische Gruppe (DE-588)4389412-4 gnd |
| topic_facet | Groepentheorie Sporadic groups (Mathematics) Finite simple groups Symmetry groups Symmetrische Gruppe Sporadische Gruppe |
| url | http://www.loc.gov/catdir/enhancements/fy0803/2007298511-b.html http://www.loc.gov/catdir/enhancements/fy0803/2007298511-d.html http://www.loc.gov/catdir/enhancements/fy0803/2007298511-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016748608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT curtisrobert symmetricgenerationofgroupswithapplicationstomanyofthesporadicfinitesimplegroups |