The Structure of Groups of Prime Power Order

The coclass project (1980-1994) provided a way to classify finite p-groups. This monograph gives an account of the thinking out of which developed the philosophy that lead to this classification. The authors provide a 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 survey of the recent and contemporary research on the structure of finite p-groups will be an important reference for all group theorists.

Review:

... there is considerable new material in this book ... The book is beautifully produced - a pleasure to the eyes, as well as to the mind, to read. Zentralblatt MATH