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Classgroups of Group Rings (Electronic book text)
Classgroups of Group Rings (Electronic book text): Martin J. Taylor

Classgroups of Group Rings (Electronic book text)

Martin J. Taylor

Series: London Mathematical Society Lecture Note Series

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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.


Imprint: Cambridge UniversityPress
Country of origin: United Kingdom
Series: London Mathematical Society Lecture Note Series
Release date: May 2013
Editors: Martin J. Taylor
Format: Electronic book text
Pages: 136
ISBN-13: 978-1-107-10774-8
Categories: Books > Science & Mathematics > Mathematics > Algebra > General
LSN: 1-107-10774-1
Barcode: 9781107107748

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