On two questions by Finch and Jones about perfect order subset groups

TL;DR

This paper investigates the properties of POS-groups, which are finite groups where element order counts divide the group order, and provides an infinite family of nonabelian POS-groups with specific order properties.

Contribution

It answers two open questions by Finch and Jones by constructing an infinite family of nonabelian POS-groups whose orders are not divisible by 3.

Findings

Constructed an infinite family of nonabelian POS-groups

Demonstrated these groups have orders not divisible by 3

Extended understanding of the structure of POS-groups

Abstract

A finite group G is said to be a POS-group if the number of elements of every order occurring in G divides |G|. We answer two questions by Finch and Jones by providing an infinite family of nonabelian POS-groups with orders not divisible by 3.