Analytic pro-p groups
By: J.D. Dixon ... [et al.].
Contributors: Dixon, John D.; Du Sautoy, Marcus.; Segal, Daniel, Ph.D.
Edition: 2nd ed. rev. and enl. / by Marcus du Sautoy & Dan Segal.
Series: Cambridge studies in advanced mathematics ;; 61
Publisher: Cambridge University Press
Published: 1999
Place of publication: Cambridge [England]; New York
Language: eng
Number of pages: 368
Subjects: Nilpotent groups; p-adic groups
Description: 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.
Notes: Includes bibliographical references (p. 362-365) and index.