Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

New paper accepted by Proceedings of the Royal Society of Edinburgh, section A – Mathematics

New paper by Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia)Compact groups in which all elements have countable right Engel sinks” has been accepted for publication in Proceedings of the Royal Society of Edinburgh, section A – Mathematics. The work was supported by Mathematical Center in Akademgorodok, FAPDF and CNPq-Brazil, and stems from the collaboration with University of Brasilia.

Abstract: A right Engel sink of an element g of a group G is a set {\mathscr R}(g) such that for every x\in G all sufficiently long commutators [\dots [[g,x],x],\dots ,x] belong to {\mathscr R}(g). (Thus, g is a right Engel element precisely when we can choose {\mathscr R}(g)={ 1}.) It is proved that if every element of a compact (Hausdorff) group G has a countable right Engel sink, then G has a finite normal subgroup N such that G/N is locally nilpotent.

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 October 14, 2020 by in grants, New publications, research.

Blog Stats

  • 23,159 hits

Archives

%d bloggers like this: