The structure of non-nilpotent CTI-groups

Abstract

A subgroup H of a group G is called a TI-subgroup if H ∩ Hg ∈ 1,H, for all g ∈ G, and a group is called a CTI-group if all of its cyclic subgroups are TI-subgroups. In this paper, we determine the structure of non-nilpotent CTI-groups. Also we will show that if G is a nilpotent CTI-group, then G is either a Hamiltonian group or a non-abelian p-group. © 2013 de Gruyter.