LMS: 185 Represttns Solvable Groups (London Mathematical Society Lecture Note Series, Series Number 185) - Softcover

Manz, Olaf

Softcover

ISBN 10: 0521397391 ISBN 13: 9780521397391

Publisher: Cambridge University Press, 2008

Synopsis

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.

About this title

Review

"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

Book Description

The role of representation theory in algebra is an important one and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. Researchers into group theory, representation theory, or both, will find that this book has much to offer.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2008
• Language: English
• ISBN 10: 0521397391
• ISBN 13: 9780521397391
• Binding: Paperback
• Number of pages: 316