The Structure of $G/\Phi(G)$ in Terms of $\sigma(G)$

Alireza Jamali; Hamid Mousavi

The Structure of $G/\Phi(G)$ in Terms of $\sigma(G)$

Group Theory 2007-05-23 v1

Authors: Alireza Jamali , Hamid Mousavi

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

Keywords

finite groups soluble groups maximal subgroups Frattini subgroup union of proper subgroups

Cite

@article{arxiv.math/0507391,
  title  = {The Structure of $G/\Phi(G)$ in Terms of $\sigma(G)$},
  author = {Alireza Jamali and Hamid Mousavi},
  journal= {arXiv preprint arXiv:math/0507391},
  year   = {2007}
}

Comments

10 pages, to appear in Algebra Colloquium

The Structure of $G/\Phi(G)$ in Terms of $\sigma(G)$

Abstract

Keywords

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