Hereditary Perfect Order Subset Groups

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 $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.