Sporadic Groups (Cambridge Tracts in Mathematics) [Paperback]

Michael Aschbacher (Author)

Book Description

ISBN-10: 0521056861 | ISBN-13: 978-0521056861 | Publication Date: March 1, 2008

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.

Editorial Reviews

Book Description

Takes a first step in a program to provide a uniform self-contained treatment of the foundational material on the sporadic finite simple groups.

Product Details

• Paperback: 332 pages
• Publisher: Cambridge University Press (March 1, 2008)
• Language: English
• ISBN-10: 0521056861
• ISBN-13: 978-0521056861
• Product Dimensions: 9 x 5.8 x 1 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #4,834,353 in Books (See Top 100 in Books)

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