Non-solvable groups generated by involutions in which every involution is left 2-Engel

Abstract

The following problem was proposed as Problem 18.57 in [4] by D.V. Lytkina: Let G be a finite 2-group generated by involutions in which [x, u, u] = 1 for every x ∈ G and every involution u ∈ G. Is the derived length of G bounded? The question asks for an upper bound on the derived length of finite 2-groups generated by involutions in which every involution (not only the generators) is left 2-Engel. We negatively answer the question. © de Gruyter 2015.