Irredundant and minimal covers of finite groups

TL;DR

This paper classifies finite non-cyclic groups where every irredundant cover by proper subgroups is also minimal, providing insights into the structure of such groups.

Contribution

It offers a complete classification of finite non-cyclic groups with the property that all irredundant covers are minimal.

Findings

Identifies all finite non-cyclic groups with irredundant covers that are minimal.

Provides structural criteria for these groups.

Enhances understanding of subgroup covers in finite group theory.

Abstract

A cover of a finite non-cyclic group $G$ is a family $\mathcal{H}$ of proper subgroups of $G$ whose union equals $G$. A cover of $G$ is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite non-cyclic groups all of whose irredundant covers are minimal.