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Twelve Sporadic Groups Book

Twelve Sporadic Groups
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  • Twelve Sporadic Groups
  • Written by author Robert Jr. Griess Jr
  • Published by Springer-Verlag New York, LLC, April 2002
  • The finite simple groups come in several infinite families (alternating groups and the groups of Lie type) plus 26 sporadic groups. The sporadic groups, discovered between 1861 and 1975, exist because of special combinatorial or arithmetic circumstances.
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Book Categories

Authors

Introduction1
Acknowledgements3
Notation for Simple Groups4
Ch. 1Background from General Group Theory5
Ch. 2Assumed Results about Particular Groups11
Ch. 3Codes24
Ch. 4The Hexacode30
Ch. 5The Golay Code36
Ch. 6Subgroups of M[subscript 24]54
Ch. 7The Ternary Golay Code and 2.M[subscript 12]76
Ch. 8Lattices88
Ch. 9The Leech Lattice and Conway Groups95
Ch. 10Subgroups of the Conway Groups; the Simple Groups of Higman-Sims, McLaughlin, Hall-Janko and Suzuki; Local Subgroups; Conjugacy Classes104
App. 10AD. G. Higman's Theory of Rank 3 Permutation Groups123
App. 10BClassification Theorems125
App. 10CTables of Stabilizers126
Ch. 11Generation Three of the Happy Family and the Pariahs146
AppSome Comments on the Atlas153
References154
Index161
List of Group Theoretic Notations168
The Orders of the Finite Simple Groups169


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