The structure of non-nilpotent CTI-groups

Abstract

Abstract.A subgroup H of a group G is called a TI-subgroup if H \ H g 2 ¹1; H º, for all g 2 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.

A note on finite groups with few TI-subgroups

“…In [2], Mousavi, Rastgoo and Zenkov characterized non-nilpotent groups all of whose cyclic subgroups are TI-subgroups. As a generalization, the first author and the third author [4] proved that G is a group all of whose non-cyclic subgroups are TI-subgroups if and only if all non-cyclic subgroups of G are normal.…”