Strongly reversible groups

Abstract

Following Thierrin [9], a group G G is called strongly reversible if for every x x , y ∈ G y \in G there are positive integers l l , m m , n n such that ( x y ) l = x m y n = y n x m {(xy)^l} = {x^m}{y^n} = {y^n}{x^m} . This paper studies the structure of strongly reversible groups.