Explicit Brauer Induction
With Applications to Algebra and Number Theory

This 1994 book gave, for the first time, an entirely algebraic treatment of the technique of Explicit Brauer Induction.

Victor P. Snaith (Author)

9780521460156, Cambridge University Press

Hardback, published 27 October 1994

424 pages
23.5 x 15.7 x 2.7 cm, 0.73 kg

Review of the hardback: '… a good introduction to explicit Brauer induction and its arithmetic applications … it will be a valuable addition to the library of anyone working on these topics.' M.E. Keating, Mathematical Reviews

Explicit Brauer Induction is an 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 1994 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 re-prove 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.

Preface
1. Representations
2. Induction theorems
3. GL2Fq
4. The class-group of a group-ring
5. A class-group miscellany
6. Complete discrete valuation fields
7. Galois module structure.

Subject Areas: Algebra [PBF]