Maximal covers of finite groups

Abstract

Let $\lambda (G)$ be the maximum number of subgroups in an irredundant covering of the finite group $G$. We prove that if $G$ is a group with $\lambda (G)⩽6$, then $G$ is supersolvable. We also describe the structure of the groups $G$ with $\lambda (G)=6$. Moreover, we show that if $G$ is a group with $\lambda (G)⩽30$, then $G$ is solvable.

Submitted to an internacional journal