The purpose of this paper is to explore non-abelian finite groups with perfect order subsets. A finite group is said to have perfect order subsets (POS) if the number of elements of each given order can divide the order of the group. The study of such groups was initiated by Carrie E. Finch and Lenny Jones. In this paper, we construct POS-groups by considering semi-direct products of cyclic groups (and sometimes quaternions).
Zhao, Hongying, "Non-Abelian Groups with Perfect Order Subsets" (2012). Mathematics Student Work. 2.