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  3. Representations of Solvable Groups
  • Cited by 186
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    • Publisher:
      Cambridge University Press
      Publication date:
      23 September 2009
      16 September 1993
      ISBN:
      9780511525971
      9780521397391
      DOI:
      https://doi.org/10.1017/CBO9780511525971
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.46kg, 316 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      London Mathematical Society Lecture Note Series (185)
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Lecture Note Series (185)
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    Book description

    Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.

    Reviews

    "This is a very readable and coherent expository monograph, aimed at mathematicians and advanced students who desire a thorough knowledge of some of the main topics in the representation theory of finite solvable groups. The book features complete proofs and extensive background material." David Gluck, Mathematical Reviews

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