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  3. Sporadic Groups
  • Cited by 32
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      March 1994
      ISBN:
      9780511665585
      9780521420495
      9780521056861
      DOI:
      https://doi.org/10.1017/CBO9780511665585
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.66kg, 332 Pages
      Dimensions:
      (228 x 153 mm)
      Weight & Pages:
      0.51kg, 332 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Cambridge Tracts in Mathematics (104)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Tracts in Mathematics (104)
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    Book description

    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.

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