# Relation Modules of Finite Groups

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*K. W. Gruenberg*

A co-publication of the AMS and CBMS

This book reproduces a course of ten lectures given by the author, Karl W. Gruenberg, at the NSF Regional Conference at the University of Wisconsin-Parkside in July 1974. The aim of the lectures was twofold: to show group theorists how the presentation theory of finite groups can nowadays be successfully approached with the help of integral representation theory, and to persuade ring theorists that here was an area of group theory well suited to applications of integral representation theory. The course was constructed so that only a modicum of either group theory or module theory would be presupposed of the audience. He has also drawn on lectures that he gave at the Australian Summer Research Institute held at the University of Sydney in 1971 and at the Australian National University at Canberra in 1974.

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#### Reviews & Endorsements

An excellent account of the theory of the relation modules of finite groups.

-- M. J. Dunwoody, Mathematical Reviews

#### Table of Contents

# Table of Contents

## Relation Modules of Finite Groups

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Preface v6 free
- Lecture 1: Introduction 18 free
- Lecture 2: The Gaschutz theory 613
- Lecture 3: Module theoretic preliminaries 1219
- Lecture 4: Projective modules 1926
- Lecture 5: Relation cores 2633
- Lecture 6: The presentation rank 3441
- Lecture 7: Swan modules 4249
- Lecture 8: Heller modules 5461
- Lecture 9: Decomposition of relation cores 6471
- Lecture 10: Epilogue 7178
- References 7784
- Explanation of, and index to, some notation and terminology 8087
- ERRATUM TO "Relation Modules of Finite Groups" 8390
- Back Cover Back Cover192