School of Mathematics & Physics, University of Lincoln
New paper by Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia) “Finite groups with Engel sinks of bounded rank” has been accepted for publication in Glasgow Mathematical Journal.
Abstract: For an element of a group , an Engel sink is a subset such that for every all sufficiently long commutators belong to . A finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group every element has an Engel sink generating a subgroup of rank , then has a normal subgroup of rank bounded in terms of such that is nilpotent.