Finite Groups With Two Irredundant Covers

TL;DR

This paper classifies finite groups that have exactly two irredundant covers, extending previous work that identified groups with only one such cover, thereby advancing understanding of subgroup covers.

Contribution

It provides a complete classification of finite groups with precisely two irredundant covers, addressing an open question in group theory.

Findings

Finite groups with two irredundant covers are fully classified.

The classification builds on Brodie's work on groups with one irredundant cover.

The results deepen understanding of subgroup cover structures in finite groups.

Abstract

An irredundant cover of a finite group $G$ is a collection of proper subgroups whose union is $G$ and which contains no smaller subcover. We classify finite groups which possess exactly two irredundant covers, thereby initiating an answer to a question of Brodie, who classified finite groups with one irredundant cover.