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.
|Country of origin:
||London Mathematical Society Lecture Note Series
Martin J. Taylor
||Electronic book text
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