Positive laws on generators in powerful pro-p groups

Details Positive laws on generators in powerful pro-p groups Positive laws on generators in powerful pro-p groups

2011-08-02

arxiv.org/abs/1108.0547v1

Mathematics

Group Theory

8 pages, to appear in Proceedings of the Ischia Group Theory Conference 2010

Scientific paper

If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class of G can be bounded in terms of the prime p, the number of generators of G, the law v=1, the width of T, and the degree of the positive law. The main interest of this result is the application to verbal subgroups: if G is a p-adic analytic pro-p group in which all values of a word w satisfy positive law, and if the verbal subgroup w(G) is powerful, then w(G) is nilpotent.

Affiliated with

Also associated with

No associations

Rating

Positive laws on generators in powerful pro-p groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive laws on generators in powerful pro-p groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive laws on generators in powerful pro-p groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-509862