The Structure of $G/Φ(G)$ in Terms of $σ(G)$

Alireza Jamali, Hamid Mousavi

Published 2005-07-19Version 1

Let $G$ be a finite group. We let $\f{m}(G)$ and $\sig(G)$ denote the number of maximal subgroups of $G$ and the least positive integer $n$ such that $G$ is written as the union of $n$ proper subgroups, respectively. In this paper we determine the structure of $G/\Phi(G)$ when $G$ is a finite soluble group with $\f{m}(G)\leq 2\sig(G)$.