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Classgroups of Group Rings : London Mathematical Society Lecture Notes - Martin J. Taylor

Classgroups of Group Rings

London Mathematical Society Lecture Notes

By: Martin J. Taylor (Editor)

Paperback

Published: 11th June 1984
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This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists.

FrĀ¶lich's description of classgroups
Character Action
Swan modules
Reduction thoery
Torsion determinants
The group logarithm
Swan modules, classgroups of exceptional groups
The Extension theorum for KoT
Adams operations for classgroups
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521278706
ISBN-10: 0521278708
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 136
Published: 11th June 1984
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 0.81
Weight (kg): 0.21