By J. D. Dixon, M. P. F. Du Sautoy, A. Mann, D. Segal

ISBN-10: 0521542189

ISBN-13: 9780521542180

**Read or Download Analytic Pro-P Groups PDF**

**Similar group theory books**

**Groups, Combinatorics and Geometry**

Because the category of finite basic teams used to be introduced in 1980 the topic has persevered to extend commencing many new parts of study. This quantity incorporates a choice of papers, either survey and examine, coming up from the 1990 Durham convention during which the wonderful development of the last decade used to be surveyed and new ambitions thought of.

This vintage e-book, initially released in 1968, relies on notes of a year-long seminar the authors ran at Princeton collage. the first target of the publication was once to provide a slightly entire presentation of algebraic features of worldwide classification box idea, and the authors comprehensive this aim spectacularly: for greater than forty years for the reason that its first booklet, the booklet has served as an final resource for lots of generations of mathematicians.

The current e-book is meant as a textbook and reference paintings on 3 themes within the name. including a quantity in growth on "Groups and Geometric research" it supersedes my "Differential Geometry and Symmetric Spaces," released in 1962. in view that that point a number of branches of the topic, rather the functionality concept on symmetric areas, have constructed considerably.

- A primer on spectral theory
- Lectures on quantum groups
- The Classification of the Finite Simple Groups
- Topological groups and rings
- Compact Semitopological Semigroups and Weakly Almost Periodic Functions

**Extra resources for Analytic Pro-P Groups**

**Example text**

Clearly g contains (g); since each element of g is the z limit of a sequence of elements of (g) it follows that g p < (g). 27 Definition A group G is procyclic if G is profinite and G/N is a cyclic group for every open normal subgroup TV of G. 28 Proposition Let G be a pro-p group. Then the following are equivalent (a) G is procyclic; (b) G can be topologically generated by a one-element subset; (c) G = gZp for some g £ G; (d) G is either finite and cyclic or else is topologically isomorphic to Proof Assume that G is procyclic, and suppose that G has two distinct maximal proper open subgroups M and N.

G. G then iVM and [JV, M] are both powerfully embedded in G. (e) G has a unique maximal powerfully embedded subgroup. 2. Let M,N

Hence M = Gn+\K, and the result follows by induction. (ii) Certainly [G^, Gi] < G*+i for all i. Let n>2 and suppose inductively that [Gi,G n _i] < Gi+n-i for all i. Now we fix m > 1, and want to show that [G m ,G n ] < G m + n . Since Grn+n is closed, it will suffice to show that [Gm,Gn] < N whenever G m + n < N <\o G. Thus, in view of (i), we may replace G by the finite p-group G/N, and assume further that G m + n = 1. Then [G m ,G n _i] < G m + n _ i is central and has exponent dividing p. If g G Gm and x G G n _i we have so[G m ,G^_ 1 ] = l.