Collaboration of algebraists in Lincoln and Brasilia produced a new paper accepted by “Journal of Pure and Applied Algebra”

The paper Compact groups in which commutators have finite right Engel sinks by Evgeny Khukhro (University of Lincoln) and Pavel Shumyatsky (University of Brasilia) has been accepted for publication in “Journal of Pure and Applied Algebra”. The results stem from long-term collaboration between the authors on finite, profinite, and compact groups satisfying Engel-type conditions.

Abstract: A right Engel sink of an element $g$ of a group $G$ is a subset containing all sufficiently long commutators $[. . . [[g,x],x],\dots ,x]$ . We prove that if $G$ is a compact group in which, for some $k$ , every commutator $[. . . [g_1,g_2],\dots ,g_k]$ has a finite right Engel sink, then $G$ has a locally nilpotent open subgroup. If in addition, for some positive integer $m$ , every commutator $[. . . [g_1,g_2],\dots ,g_k]$ has a right Engel sink of cardinality at most $m$ , then $G$ has a locally nilpotent subgroup of finite index bounded in terms of $m$ only.