Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

Paper accepted for publication

IJAC-coverThe paper by E. I. Khukhro and P. Shumyatsky, Almost Engel finite and profinite groups  has been accepted for publication in the International  Journal of Algebra and Computation, ISSN  0218-1967, see also arXiv:1512.06097.

Abstract: Let g be an element of a group G. For a positive integer n, let E_n(g) be the subgroup generated by all commutators [...[[x,g],g],\dots, g] over x\in G, where g is repeated n times. We prove that if G is a profinite group such that for every g\in G there is n=n(g) such that E_n(g) is finite, then G has a finite normal subgroup N such that G/N is locally nilpotent. The proof uses the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent. In the case of a finite group G, we prove that if, for some n, |E_n(g)|\leq m for all g\in G, then the order of the nilpotent residual \gamma _{\infty} (G) is bounded in terms of m.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Information

This entry was posted on June 5, 2016 by in New publications, News and announcements.

Blog Stats

  • 22,780 hits

Archives

%d bloggers like this: