A note on subgroup coverings of finite groups

TL;DR

This paper characterizes finite groups that can be expressed as unions of three proper subgroups, focusing on those with unique such decompositions, advancing understanding of subgroup structures.

Contribution

It identifies all finite groups that are unions of three irredundant subgroups and those with unique such unions, providing new classifications in group theory.

Findings

Finite groups that can be written as the union of three irredundant proper subgroups.

Finite groups with a unique union of three proper subgroups.

Complete classification of such groups.

Abstract

In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.