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Sporadic Groups : Cambridge Tracts in Mathematics (Hardcover) - Michael Aschbacher

Sporadic Groups

Cambridge Tracts in Mathematics (Hardcover)

Hardcover Published: 11th January 2006
ISBN: 9780521420495
Number Of Pages: 332

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Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups, such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits plus a few new wrinkles. The existence treatment finishes with an application of the theory of large extraspecial subgroups to produce the twenty sporadics involved in the Monster. The Aschbacher-Segev approach addresses the uniqueness of the sporadics via coverings of graphs and simplicial complexes. The basics of this approach are developed and used to establish the uniqueness of five of the sporadics.

Preface
Preliminary results
2-Structure in finite groups
Algebras, codes and forms
Symplectic 2-loops
The discovery, existence, and uniqueness of the sporadics
The Mathieu groups, their Steiner systems, and the Golay code
The geometry and structure of M24
The Conway groups and the Leech lattice
Subgroups of .0
The Griess algebra and the Monster
Subgroups of groups of Monster type
Coverings of graphs and simplicial complexes
The geometry of amalgams
The uniqueness of groups of type M24, He, and L5(2)
The groups U4(3)
Groups of Conway, Suzuki, and Hall-Janko type
Subgroups of prime order in five sporadic groups
Tables
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521420495
ISBN-10: 0521420490
Series: Cambridge Tracts in Mathematics (Hardcover)
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 332
Published: 11th January 2006
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.52 x 16.15  x 2.67
Weight (kg): 0.64

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