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Main Author:	Aschbacher, Michael 1944- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 1994
Edition:	1. publ.
Series:	Cambridge tracts in mathematics 104
Subjects:	Sporadic groups (Mathematics) Sporadische Gruppe Gruppe > Mathematik
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 314 S.
ISBN:	0521420490 9780521420495 9780521056861

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MARC


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adam_text	Contents Preface page ix PART I 1. Preliminary Results 1 1. Abstract representations 1 2. Permutation representations 2 3. Graphs 4 4. Geometries and complexes 6 5. The general linear group and its projective geometry 13 6. Fiber products of groups 15 2. 2 Structure in Finite Groups 18 7. Involutions 18 8. Extraspecial groups 21 3. Algebras, Codes, and Forms 35 9. Forms and algebras 36 10. Codes 40 11. Derived forms 41 4. Symplectic 2 Loops 46 12. Symplectic 2 loops 47 13. Moufang symplectic 2 loops 54 14. Constructing a 2 local from a loop 57 5. The Discovery, Existence, and Uniqueness of the Sporadics 65 15. History and discovery 65 16. Existence of the sporadics 70 17. Uniqueness of the sporadics 74 PART II 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code 77 18. Steiner systems for the Mathieu groups 78 19. The Golay and Todd modules 85 vi Contents 7. The Geometry and Structure of M24 96 20. The geometry of M24 96 21. The local structure of M24 103 8. The Conway Groups and the Leech Lattice 108 22. The Leech lattice and • 0 108 23. The Leech lattice mod 2 116 9. Subgroups of • 0 124 24. The groups C03, Me, and HS 125 25. The groups Co , C02, Suz, and Ji 132 26. Some local subgroups of Co 135 10. The Griess Algebra and the Monster 142 27. The subgroups C and N of the Monster 143 28. The Griess algebra 151 29. The action of N on B 154 30. N preserves the Griess algebra 162 31. The automorphism group of the Griess algebra 167 11. Subgroups of Groups of Monster Type 172 32. Subgroups of groups of Monster type 173 PART III 12. Coverings of Graphs and Simplicial Complexes 175 33. The fundamental groupoid 176 34. Triangulation 182 35. Coverings of graphs and simplicial complexes 184 13. The Geometry of Amalgams 194 36. Amalgams 195 37. Uniqueness systems 198 38. The uniqueness system of a string geometry 204 14. The Uniqueness of Groups of Type M24, He, and Z5(2) 212 39. Some 2 local subgroups in £5(2), M24, and He 213 40. Groups of type £5(2), M24, and He 216 41. Groups of type L5 (2) and M24 219 42. Groups of type He 223 43. The root 4 group graph for He 230 44. The uniqueness of groups of type He 236 Contents vii 15. The Group C74(3) 241 45. U4(3) 242 16. Groups of Conway, Suzuki, and Hall—Janko Type 250 46. Groups of type Co , Suz, J2, and J3 250 47. Groups of type J2 259 48. Groups of type Suz 267 49. Groups of type Co 279 17. Subgroups of Prime Order in Five Sporadic Groups 293 50. Subgroups of Suz of prime order 293 51. Subgroups of Co of prime order 295 52. Subgroups of prime order in He 299 Symbols 304 Bibliography 306 Index 311
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discipline	Mathematik
edition	1. publ.
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indexdate	2024-07-09T17:38:50Z
institution	BVB
isbn	0521420490 9780521420495 9780521056861
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-006390692
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owner	DE-384 DE-12 DE-29T DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-703 DE-20 DE-19 DE-BY-UBM DE-11 DE-188 DE-83 DE-824
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physical	XII, 314 S.
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spelling	Aschbacher, Michael 1944- Verfasser (DE-588)142400955 aut Sporadic groups Michael Aschbacher 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1994 XII, 314 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 104 Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Sporadische Gruppe (DE-588)4389412-4 s DE-604 Gruppe Mathematik (DE-588)4022379-6 s Cambridge tracts in mathematics 104 (DE-604)BV000000001 104 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006390692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Aschbacher, Michael 1944- Sporadic groups Cambridge tracts in mathematics Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd
subject_GND	(DE-588)4389412-4 (DE-588)4022379-6
title	Sporadic groups
title_auth	Sporadic groups
title_exact_search	Sporadic groups
title_full	Sporadic groups Michael Aschbacher
title_fullStr	Sporadic groups Michael Aschbacher
title_full_unstemmed	Sporadic groups Michael Aschbacher
title_short	Sporadic groups
title_sort	sporadic groups
topic	Sporadic groups (Mathematics) Sporadische Gruppe (DE-588)4389412-4 gnd Gruppe Mathematik (DE-588)4022379-6 gnd
topic_facet	Sporadic groups (Mathematics) Sporadische Gruppe Gruppe Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006390692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000001
work_keys_str_mv	AT aschbachermichael sporadicgroups

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