The Structure of Groups of Prime Power Order

Hardcover | July 1, 2002

byC.R. Leedham-Green, S. McKay

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The coclass project (1980-1994) provided a new and powerful way to classify finite p-groups. This monograph gives a coherent account of the thinking from which the philosophy that lead to this classification developed. The authors provide a careful summary and explanation of the many anddifficult original research papers on the coclass conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers. The classification philosophy has lead to many new and challenging problems. Amongst those considered are problems about pro-p-groups, the Grigorchuk group, the Nottingham group as well as linear pro-p-groups. Throughout the book the authors have used a wide range of algebraic techniques and have developed from first principles, or from basic and well known results, the cohomology of groups, spectral sequences, and representation theory. This comprehensive and long-awaited survey of the recent and current research on the structure of finite p-groups will be an important reference for all group theorists.

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From the Publisher

The coclass project (1980-1994) provided a new and powerful way to classify finite p-groups. This monograph gives a coherent account of the thinking from which the philosophy that lead to this classification developed. The authors provide a careful summary and explanation of the many anddifficult original research papers on the coclass...

C.R. Leedham-Green is a Professor of Pure Mathematics, Queen Mary, University of London. S. McKay is a Lecturer, School of Mathematical Sciences, Queen Mary, University of London.
Format:HardcoverDimensions:346 pages, 9.21 × 6.14 × 0.94 inPublished:July 1, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198535481

ISBN - 13:9780198535485

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Table of Contents

1. Preliminaries2. New groups from old3. p-groups of maximal class4. Finite p-groups acting uniserially5. Lie Methods6. The proof of Conjecture A7. Pro-p-groups8. Constructing finite p-groups9. Homological algebra10. Uniserial p-adic space groups11. The structure of finite p-groups12. Beyond coclassBibliographySymbol indexindex

Editorial Reviews

"This book is beautifully produced--a pleasure to the eyes as well as the mind."--Mathematical Reviews