Author Aschbacher, Michael, 1944- author
Title Sporadic groups / Michael Aschbacher
Imprint Cambridge : Cambridge University Press, 1994
book jacket
Descript 1 online resource (xii, 314 pages) : digital, PDF file(s)
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
text file PDF rda
Series Cambridge tracts in mathematics ; 104
Cambridge tracts in mathematics ; 104
Note Title from publisher's bibliographic system (viewed on 05 Oct 2015)
1. Preliminary Results -- 2. 2-Structure in Finite Groups -- 3. Algebras, Codes, and Forms -- 4. Symplectic 2-Loops -- 5. The Discovery, Existence, and Uniqueness of the Sporadics -- 6. The Mathieu Groups, Their Steiner Systems, and the Golay Code -- 7. The Geometry and Structure of M[subscript 24] -- 8. The Conway Groups and the Leech Lattice -- 9. Subgroups of [actual symbol not reproducible] -- 10. The Griess Algebra and the Monster -- 11. Subgroups of Groups of Monster Type -- 12. Coverings of Graphs and Simplicial Complexes -- 13. The Geometry of Amalgams -- 14. The Uniqueness of Groups of Type M[subscript 24], He, and L[subscript 5](2) -- 15. The Group U[subscript 4](3) -- 16. Groups of Conway, Suzuki, and Hall-Janko Type -- 17. Subgroups of Prime Order in Five Sporadic Groups
Sporadic 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
Subject Sporadic groups (Mathematics)