02573nmm a2200277 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001000139100001900149245005700168250001900225260004800244300003000292505082200322653002101144653001801165041001901183989003201202490004601234856006301280082001001343520094201353EB001382937EBX0100000000000000090590200000000000000.0cr|||||||||||||||||||||170324 ||| eng a9780511470882 4aQA1771 aDixon, John D.00aAnalytic pro-p groupscJ.D. Dixon [and three others] aSecond edition aCambridgebCambridge University Pressc1999 axviii, 368 pagesbdigital0 aPt. 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 -- Pt. 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 Poincare series -- 9. Lie theory -- Pt. III. Further topics -- 10. Pro-p groups of finite coclass -- 11. Dimension subgroup methods -- 12. Some graded algebras -- Interlude D. The Golod-Shafarevich inequality -- Interlude E. Groups of sub-exponential growth -- 13. Analytic groups over pro-p rings -- App. A. The Hall-Petrescu formula -- App. B. Topological groups aNilpotent groups ap-adic groups07aeng2ISO 639-2 bCBOaCambridge Books Online0 aCambridge studies in advanced mathematics uhttps://doi.org/10.1017/CBO9780511470882xVerlag3Volltext0 a512.2 aThe 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