Representations of solvable groups
By: Olaf Manz and Thomas R. Wolf.
Contributors: Wolf, Thomas R.
Series: London Mathematical Society lecture note series ;; 185
Publisher: Cambridge University Press
Published: 1993
Place of publication: Cambridge; New York
Language: eng
Number of pages: 302
Subjects: Solvable groups.; Representations of groups.; Permutation groups.
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.
Notes: Includes bibliographical references (p. 293-298) and index.