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

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

2005-07-19

arxiv.org/abs/math/0507391v1

Mathematics

Group Theory

10 pages, to appear in Algebra Colloquium

Scientific paper

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
$\f{m}(G)\leq 2\sig(G)$.

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