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.
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The theory of p-adic analytic pro-p groups has undergone significant development since the seminal work of Lazard. This book presents a complete and self-contained account of this theory, which has applications in both group theory and number theory. This up-to-date second edition incorporates many important new results.Contenuti:
Prelude; Part I. Pro-p Groups: 1. Profinite groups and pro-p groups; 2. Powerful p-groups; 3. Pro-p groups of finite rank; 4. Uniformly powerful groups; 5. Automorphism groups; Interlude A. Fascicule de resultats: pro-p groups of finite rank; Part II. Analytic Groups: 6. Normed algebras; 7. The group algebra; Interlude B. Linearity criteria; 8. P-adic analytic groups; Interlude C. Finitely generated groups, p-adic analytic groups and Poincaré series; 9. Lie theory; Part III. Further Topics: 10. Pro-p groups of finite co-class; 11. Dimension subgroup methods; 12. Some graded algebras; Interlude D. The Golod Shafarevic inequality; Interlude E. Groups of sub-exponential growth; 13. Analytic groups over pro-p rings.
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