Explicit Brauer Induction: With Applications to Algebra and Number Theory

Explicit Brauer Induction: With Applications to Algebra and Number Theory

by Victor P. Snaith
     
 

ISBN-10: 052117273X

ISBN-13: 9780521172738

Pub. Date: 02/17/2011

Publisher: Cambridge University Press

Explicit Brauer Induction is a new and important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this book it is derived algebraically, following a method of R. Boltje--thereby making the technique, previously topological, accessible to algebraists. Once developed, the…  See more details below

Overview

Explicit Brauer Induction is a new and important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this book it is derived algebraically, following a method of R. Boltje--thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to reprove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver-Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.

Product Details

ISBN-13:
9780521172738
Publisher:
Cambridge University Press
Publication date:
02/17/2011
Series:
Cambridge Studies in Advanced Mathematics Series, #40
Edition description:
Reissue
Pages:
422
Product dimensions:
6.00(w) x 8.90(h) x 1.20(d)

Table of Contents

Preface
1Representations1
2Induction theorems23
3GL[subscript 2]F[subscript q]72
4The class-group of a group-ring106
5A class-group miscellany170
6Complete discrete valuation fields245
7Galois module structure299
Bibliography403
Index407

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