Analytic Pro-P Groups (London Mathematical Society Lecture Note Series, Series Number 157) - Softcover

Dixon, J. D.; Sautoy, M. D. F.; Mann, A.; Segal, D.

Softcover

ISBN 10: 0521395801 ISBN 13: 9780521395809

Publisher: Cambridge University Press, 1991

Synopsis

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.

About this title

Synopsis:

An examination of analytic pro-rho groups from the perspectives of both Lie theory and the theory of pro-rho groups. Intended as an introduction to some powerful new methods in group theory, this book also presents an algebraic account of the foundations and basic results in rho-adic Lie groups.

About this edition

• Publisher: Cambridge University Press
• Publication date: 1991
• ISBN 10: 0521395801
• ISBN 13: 9780521395809
• Binding: Paperback
• Number of pages: 261