Sporadic Groups by Michael Aschbacher (English) Hardcover Book

Description: Sporadic Groups by Michael Aschbacher 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 authors 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. Author Biography Michael Aschbacher is the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology. Table of Contents Preface; 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 M24; 8. The Conway groups and the Leech lattice; 9. Subgroups of .0; 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 M24, He, and L5(2); 15. The groups U4(3); 16. Groups of Conway, Suzuki, and Hall-Janko type; 17. Subgroups of prime order in five sporadic groups; Tables; References; Index. Promotional "Headline" The first self-contained treatment of the foundations of the theory of sporadic groups. Description for Bookstore 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 authors text Finite Group Theory. Description for Library 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 authors text Finite Group Theory. Details ISBN0521420490 Author Michael Aschbacher Short Title SPORADIC GROUPS Pages 332 Publisher Cambridge University Press Series Cambridge Tracts in Mathematics (Hardcover) Language English ISBN-10 0521420490 ISBN-13 9780521420495 Media Book Format Hardcover DEWEY 512.2 Series Number 104 Year 1994 Publication Date 1994-03-31 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Illustrations tavles, references, index Birth 1944 Affiliation California Institute of Technology DOI 10.1604/9780521420495 Audience Professional and Scholarly UK Release Date 1994-03-25 AU Release Date 1994-03-25 NZ Release Date 1994-03-25 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91365722;

Price: 300.6 AUD

Location: Melbourne

End Time: 2025-02-08T03:37:00.000Z

Shipping Cost: 12.1 AUD