Analytic Pro-P Groups

An analytic pro-p group can be viewed from the contrasting perspectives of Lie theory or the theory of pro-p groups. Each viewpoint gives rise to powerful results, and in this account the authors exploit both perspectives. The book begins by developing the theory of pro-p groups using only elementary group-theoretic notions. Several characterizations of pro-p groups of finite rank are given and an intrinsic construction for the associated Lie algebra gives a faithful linear representation for the automorphism groups of such groups. There follows a description of some striking recent applications of these results in group theory, including Lubotsky's characterization of finitely generated linear groups. The second part of the book develops the theory of p-adic analytic groups by building on the results of Part I. The analysis is linked by the fact that a compact p-adic analytic group is virtually a pro-p group of finite rank. All the main features of p-adic Lie theory are then derived.