Holdings: Geometry of sporadic groups

Geometry of sporadic groups: 2 Representations and amalgams

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Bibliographic Details
Main Authors:	Ivanov, A. A. (Author), Špektorov, Sergej V. (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2002
Edition:	1. publ.
Series:	Encyclopedia of mathematics and its applications 91
Subjects:	Sporadic groups (Mathematics)
Online Access:	Inhaltsverzeichnis
Physical Description:	XVIII, 286 S. graph. Darst.
ISBN:	0521623499

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adam_text	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS FOUNDED BY G.-C. ROTA EDITORIAL BOARD R. S. DORAN, P. FLAJOLET, M. ISMAIL, T.-Y. LAM, E. LUTWAK, R. SPIGLER VOLUME 91 GEOMETRY OF SPORADIC GROUPS II REPRESENTATIONS AND AMALGAMS CONTENTS PREFACE PAGE IX 1 PRELIMINARIES 1 1.1 GEOMETRIES AND DIAGRAMS 1 1.2 COVERINGS OF GEOMETRIES 3 1.3 AMALGAMS OF GROUPS 5 1.4 SIMPLE CONNECTEDNESS VIA UNIVERSAL COMPLETION 7 1.5 REPRESENTATIONS OF GEOMETRIES 11 PART I. REPRESENTATIONS 17 2 GENERAL FEATURES 19 2.1 TERMINOLOGY AND NOTATION 19 2.2 COLLINEARITY GRAPH 22 2.3 GEOMETRIC HYPERPLANES 24 2.4 ODD ORDER SUBGROUPS 27 2.5 CAYLEY GRAPHS 32 2.6 HIGHER RANKS - 34 2.7 C-EXTENSIONS : 35 2.8 NON-SPLIT EXTENSIONS 40 3 CLASSICAL GEOMETRIES 43 3.1 LINEAR GROUPS 43 3.2 THE GRASSMANIAN ) - 45 3.3 0 IS UNISERIAL 47 3.4 ^(S 4 (2)) 50 3.5 SYMPLECTIC GROUPS 51 3.6 ORTHOGONAL GROUPS 55 3.7 BROUWER S CONJECTURE 56 3.8 ^(3-S 4 (2)) ... 64 VI CONTENTS 3.9 3.10 4 4.1 4.2 4.3 4.4 4.5 4.6 5 5.1 5.2 5.3 5.4 5.5 5.6 6 6.1 6.2 6.3 6.4 6.5 6.6 7 7.1 7.2 7.3 7.4 7.5 7.6 - 7.7 7.8 7.9 9(ALT 5 ) 9(3GJ J 52,(2)) MATHIEU GROUPS AND HELD GROUP 3(M 2 T,) ^(M 22 ) ^(M 24 ) ^(3-M 22 ) 9(HE) CONWAY GROUPS LEECH LATTICE @(CO 2 ) 9(COI) ABELIANIZATION 0(3 23 * CO 2 ) 9(3 * C/ 4 (3)) INVOLUTION GEOMETRIES GENERAL METHODS J(A TI) J(M 22 ) ./(L/ 4 (3)) J{CO 2 ,2B) J(CO U 2A) LARGE SPORADICS EXISTENCE OF THE REPRESENTATIONS A REDUCTION VIA SIMPLE CONNECTEDNESS THE STRUCTURE OF N(P) IDENTIFYING RI(P) R (P) IS NORMAL IN R[P R _P IS ISOMORPHIC TO G(P) GENERATION OF G(P) N G(Q) RECONSTRUCTING THE RANK 3 AMALGAM ^(3 4371 * BM) 111 111 115 117 120 122 125 128 128 131 134 141 146 151 153. 155 159 PART II. AMALGAMS 161 8 METHOD OF GROUP AMALGAMS 163 8.1 GENERAL STRATEGY 163 8.2 SOME COHOMOLOGIES 165 CONTENTS VII 8.3 GOLDSCHMIDT S THEOREM 170 8.4 FACTOR AMALGAMS 173 8.5 L 3 (2)-LEMMA 175 8.6 TWO PARABOLICS ARE SUFFICIENT 178 180 180 183 187 191 196 198 198 200 204 209 211 211 213 215 215 217 219 221 - 227 233 , 234 242 242 243 246 248 253 256 261 261 CONCLUDING REMARKS 269 9 9.1 9.2 9.3 9.4 9.5 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 ACTION ON THE DERIVED GRAPH A GRAPH THEORETICAL SETUP NORMAL SERIES OF THE VERTEX STABILIZER CONDITION (;) NORMAL SERIES OF THE POINT STABILIZER PUSHING UP SHAPES OF AMALGAMS THE SETTING RANK THREE CASE RANK FOUR CASE RANK FIVE CASE RANK SIX CASE THE SYMPLECTIC SHAPE SUMMARY AMALGAMS FOR P -GEOMETRIES M 22 -SHAPE AUT M 22 -SHAPE M 2 3-SHAPE CO 2 -SHAPE J 4 -SHAPE TRUNCATED J 4 -SHAPE BM-SHAPE AMALGAMS FOR T-GEOMETRIES ALTY-SHAPE S 6 (2)-SHAPE M 24 -SHAPE TRUNCATED M 24 -SHAPE THE COMPLETION OF STFF CO -SHAPE M-SHAPE S 2N (2)-SHAPE, N 4 VIII CONTENTS 13 FURTHER DEVELOPMENTS 271 13.1 GROUP-FREE CHARACTERIZATIONS 271 13.2 LOCALLY PROJECTIVE GRAPHS 275 REFERENCES 278 INDEX . S 285
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author	Ivanov, A. A. Špektorov, Sergej V.
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series	Encyclopedia of mathematics and its applications
series2	Encyclopedia of mathematics and its applications
spelling	Ivanov, A. A. Verfasser aut Geometry of sporadic groups 2 Representations and amalgams A. A. Ivanov ; S. V. Shpectorov 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2002 XVIII, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 91 Encyclopedia of mathematics and its applications ... Sporadic groups (Mathematics) Špektorov, Sergej V. Verfasser aut (DE-604)BV012683455 2 Encyclopedia of mathematics and its applications 91 (DE-604)BV000903719 91 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010485976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ivanov, A. A. Špektorov, Sergej V. Geometry of sporadic groups Encyclopedia of mathematics and its applications Sporadic groups (Mathematics)
title	Geometry of sporadic groups
title_auth	Geometry of sporadic groups
title_exact_search	Geometry of sporadic groups
title_full	Geometry of sporadic groups 2 Representations and amalgams A. A. Ivanov ; S. V. Shpectorov
title_fullStr	Geometry of sporadic groups 2 Representations and amalgams A. A. Ivanov ; S. V. Shpectorov
title_full_unstemmed	Geometry of sporadic groups 2 Representations and amalgams A. A. Ivanov ; S. V. Shpectorov
title_short	Geometry of sporadic groups
title_sort	geometry of sporadic groups representations and amalgams
topic	Sporadic groups (Mathematics)
topic_facet	Sporadic groups (Mathematics)
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010485976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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