Soluble groups with few conjugate classes of non-cyclic subgroups

Abstract

For a group [Formula: see text], let [Formula: see text] be the number of conjugate classes of the non-cyclic subgroups. In this paper, we prove that the derived length of the group [Formula: see text] with [Formula: see text] is at most 3, and we also study the non-nilpotent group [Formula: see text] with [Formula: see text].