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

Alireza Jamali·Hamid Mousavi
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Abstract

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 $G/Φ(G)$ when $G$ is a finite soluble group with $\f{m}(G)\leq 2\sig(G)$.

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Alireza Jamali, Hamid Mousavi. 2005-07-19. The Structure of $G/Φ(G)$ in Terms of $σ(G)$. https://arxiv.org/abs/math/0507391

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