Representations of Solvable Groups
Representations of Solvable Groups by Olaf Manz, published by Cambridge University Press on September 16, 1993, is a comprehensive exploration of representation theory as it pertains to solvable groups. This edition spans 302 pages and is presented in English. The authors focus on modules over finite fields, which are integral to understanding the structure of solvable groups, and they delve into character theory, including both ordinary and Brauer aspects.
Readers will find a detailed examination of significant conjectures, including proofs of Brauer’s height zero conjecture and the Alperin-McKay conjecture specifically for solvable groups. The book also discusses Gluck’s permutation lemma and Huppert’s classification of solvable two-transitive permutation groups, emphasizing their relevance to finite modules of finite groups. This work serves as a valuable resource for researchers engaged in group theory and representation theory, providing insights and applications that enhance the understanding of these mathematical concepts.
Official synopsis Publisher
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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