Analytic Pro-P Groups

The first edition of this book was the indispensable reference for researchers in the theory of pro-p groups. In this second edition the presentation has been improved and important new material has been added. The first part of the book is group-theoretic. It develops the theory of pro-p groups of finite rank starting from first principles and using elementary methods. Part II introduces p-adic analytic groups: by taking advantage of the theory developed in Part I it is possible to define these and derive all the main results of p-adic Lie theory without having to develop any sophisticated analytic machinery. Part III consisting of new material takes the theory further. Among those topics discussed are the theory of pro-p groups of finite coclass the dimension subgroup series and its associated graded Lie algebra. The final chapter sketches a theory of analytic groups over pro-p rings other than the p-adic integers.