Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

A paper accepted by “Quarterly Journal of Mathematics (Oxford)”

A new paper by Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia) “Compact groups in which all elements are almost right Engel” has been accepted for publication in Quarterly Journal of Mathematics (Oxford). The results of this paper were partially obtained during Evgeny Khukhro’s research visit to University of Brasilia in July of 2018 (supported by a grant of CNPq-Brazil).

Abstract: An element g of a group G is said to be almost right Engel if there is a finite set {\mathscr R}(g) such that for every x\in G there is a positive integer n(x,g) such that [...[[g,x],x],\dots ,x]\in {\mathscr R}(g) if x is repeated at least n(x,g) times. Thus, g is a right Engel element precisely when we can choose {\mathscr R}(g)=\{ 1\}.

We prove that if all elements of a compact (Hausdorff) group G are almost right Engel, then G has a finite normal subgroup N such that G/N is locally nilpotent. If in addition there is a uniform bound |{\mathscr R}(g)|\leq m for the orders of the corresponding sets, then the subgroup N can be chosen of order bounded in terms of m. The proofs use the Wilson–Zelmanov theorem saying that profinite Engel groups are locally nilpotent and previous results of the authors about compact groups in which all elements are almost left Engel.

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 January 27, 2019 by in New publications, research.
%d bloggers like this: