By (author) Michael Aschbacher
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Sporadic Groups by Michael Aschbacher
Book DescriptionSporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. 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. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.
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Book DetailsISBN: 9780521056861
(229mm x 152mm x 19mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 1-Mar-2008
Country of Publication: United Kingdom
Books By Author Michael Aschbacher
Fusion Systems in Algebra and Topology, Paperback (August 2011)
This book combines a detailed exposition of the basics of fusion systems with a survey of the current state of the field.
3-transposition Groups, Paperback (February 2009)
Contains the first complete published proof of Fischer's Theorem on the classification of 3-transposition groups.
Proceedings of the Rutgers Group Theory Year, 1983 -1984, Paperback (December 2008)
In this symposium volume twenty-nine key figures in the classification programme analyse the likely directions research will take in the future.
Finite Group Theory, Hardback (July 2000)» View all books by Michael Aschbacher
The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.
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