Analytic Pro-P Groups

An up-to-date treatment of analytic pro-p groups for graduate students and researchers.

Zusammenfassung
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.

Inhalt

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.