Covering certain monolithic groups with proper subgroups

Martino Garonzi

paper

Covering certain monolithic groups with proper subgroups

arXiv:1211.5345

Abstract

Given a finite non-cyclic group $G$ , call $σ (G)$ the least number of proper subgroups of $G$ needed to cover $G$ . In this paper we give lower and upper bounds for $σ (G)$ for $G$ a group with a unique minimal normal subgroup $N$ isomorphic to $A_{n}^{m}$ where $n \geq 5$ and $G / N$ is cyclic. We also show that $σ (A_{5} ≀ C_{2}) = 57$ .

Communications in Algebra (2012)