Finite groups determined by an inequality of the orders of their subgroups II

TL;DR

This paper investigates finite groups with specific subgroup order inequalities, providing characterizations of groups like Z2×Z2 and S3, thereby advancing understanding of their structural properties.

Contribution

It offers new characterizations of certain finite groups based on inequalities involving subgroup orders, extending previous work in the area.

Findings

Characterization of Z2×Z2 groups

Characterization of S3 groups

Identification of subgroup order inequalities

Abstract

In this note we study a class of finite groups for which the orders of subgroups satisfy a certain inequality. In particular, characterizations of the well-known groups $\mathbb{Z}_2\times\mathbb{Z}_2$ and $S_3$ are obtained.