Representations of Solvable Groups

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Cambridge University Press, Sep 16, 1993 - Mathematics - 302 pages
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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.
  

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Contents

Chap I Solvable subgroups of linear groups
27
Chap II Solvable permutation groups
73
Chap Ill Module actions with large centralizers
117
Chap IV Prime power divisors of character degrees
157
Chap V Complexity of character degrees
210
Chap VI πspecial characters
265
References
293
Index
299
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