{"product_id":"sporadic-groups-hardback-9780521420495","title":"Sporadic Groups (Hardback) 9780521420495","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSporadic Groups\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe first self-contained treatment of the foundations of the theory of sporadic groups.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichael Aschbacher (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521420495, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 25 March 1994\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e332 pages\u003cbr\u003e22.9 x 15.2 x 2.2 cm, 0.66 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eSporadic 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Preliminary results\u003cbr\u003e 2. 2-Structure in finite groups\u003cbr\u003e 3. Algebras, codes and forms\u003cbr\u003e 4. Symplectic 2-loops\u003cbr\u003e 5. The discovery, existence, and uniqueness of the sporadics\u003cbr\u003e 6. The Mathieu groups, their Steiner systems, and the Golay code\u003cbr\u003e 7. The geometry and structure of M24\u003cbr\u003e 8. The Conway groups and the Leech lattice\u003cbr\u003e 9. Subgroups of .0\u003cbr\u003e 10. The Griess algebra and the Monster\u003cbr\u003e 11. Subgroups of groups of Monster type\u003cbr\u003e 12. Coverings of graphs and simplicial complexes\u003cbr\u003e 13. The geometry of amalgams\u003cbr\u003e 14. The uniqueness of groups of type M24, He, and L5(2)\u003cbr\u003e 15. The groups U4(3)\u003cbr\u003e 16. Groups of Conway, Suzuki, and Hall-Janko type\u003cbr\u003e 17. Subgroups of prime order in five sporadic groups\u003cbr\u003e Tables\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Groups \u0026amp; group theory [\u003ca title=\"See our other books on Groups \u0026amp; group theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Groups%20\u0026amp;%20group%20theory%20%5BPBG%5D%22\"\u003ePBG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46007270539544,"sku":"9780521420495","price":108.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521420495i_aa40e2cd-2c28-49f2-8f0d-ada5b98e62b3.jpg?v=1691381438","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/sporadic-groups-hardback-9780521420495","provider":"Freshly Printed Books","version":"1.0","type":"link"}