Pos Groups Revisited

Abstract

A finite group $G$ is said to be a POS-group if for each $x$ in $G$ the cardinality of the set $\{y\in G|o(y)=o(x)\}$ is a divisor of the order of $G$. In this paper we study some of the properties of arbitrary POS-groups, and construct a couple of new families of nonabelian POS-groups. We also prove that the alternating group $A_n$, $n\ge 3$, is not a POS-group.

9 pages, new results and new references included