The Structure of Groups of Prime Power Order

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 out of which developed the philosophy that lead to this classification. The authors provide a careful summary and explanation of the many and
difficult 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.

1 - Preliminaries
2 - New groups from old
3 - p-groups of maximal class
4 - Finite p-groups acting uniserially
5 - Lie Methods
6 - The proof of Conjecture A
7 - Pro-p-groups
8 - Constructing finite p-groups
9 - Homological algebra
10 - Uniserial p-adic space groups
11 - The structure of finite p-groups
12 - Beyond coclass