Bounded Engel elements in residually finite groups satisfying an identity. Issue 6 (23rd January 2021) - Bastos, Raimundo; Silveira, Danilo
Abstract: Let G be a m -generator residually finite group. We show that: 1) if every γk -value in G is right n -Engel, then γ k ( G ) is s -Engel for some k, m, n -bounded number s ; 2) if G satisfies an identity w ≡ 1 and G can be generated by a commutator-closed set of left n -Engel elements, then G has m, n, w -bounded class. 3) if G has a specific generating set X in which some power of each element in X is a bounded left Engel, then G is virtually nilpotent.