Whitehead Groups of Finite Groups

Robert Oliver

doi:10.1017/CBO9780511600654

This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area.

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Whitehead Groups of Finite Groups

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Contents

Frontmatter
pp i-viii

Contents
pp ix-x

Introduction
pp 1-19

Part I - General theory
pp 20-20

Chapter 1 - Basic algebraic background
pp 21-39

Chapter 2 - Structure theorems for K1 of orders
pp 40-62

Chapter 3 - Continuous K2 and localization sequences
pp 63-89

Chapter 4 - The congruence subgroup problem
pp 90-126

Chapter 5 - First applications of the congruence subgroup problem
pp 127-152

Chapter 6 - The integral p–adic logarithm
pp 153-171

Part II - Group rings of p–groups
pp 172-172

Chapter 7 - The torsion subgroup of Whitehead groups
pp 173-182

Chapter 8 - The p–adic quotient of SK1(ℤ[G]): p–groups
pp 183-204

Chapter 9 - Cl1(ℤ[G]) for p–groups
pp 205-228

Chapter 10 - The torsion free part of Wh(G)
pp 229-242

Part III - General finite groups
pp 243-244

Chapter 11 - A quick survey of induction theory
pp 245-271

Chapter 12 - The p–adic quotient of SK1(ℤ[G]): finite groups
pp 272-290

Chapter 13 - Cl1(ℤ[G]) for finite groups
pp 291-327

Chapter 14 - Examples
pp 328-339

References
pp 340-347

Index
pp 348-349

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Whitehead Groups of Finite Groups

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