Recognizing $\mathrm{PSL}(2,p)$ in the non-Frattini chief factors of finite groups

Duong Hoang Dung

Recognizing $\mathrm{PSL}(2,p)$ in the non-Frattini chief factors of finite groups

Group Theory 2015-08-17 v2

Authors: Duong Hoang Dung

Abstract

Given a finite group $G$ , let $P_G(s)$ be the probability that $s$ randomly chosen elements generate $G$ , and let $H$ be a finite group with $P_G(s)=P_H(s)$ . We show that if the nonabelian composition factors of $G$ and $H$ are $\mathrm{PSL}(2,p)$ for some non-Mersense prime $p\geq 5$ , then $G$ and $H$ have the same non-Frattini chief factors.

Keywords

finite groups generation probability PSL(2,p) non-Frattini chief factors composition factors nonabelian simple groups non-Mersense prime

Cite

@article{arxiv.1502.05080,
  title  = {Recognizing $\mathrm{PSL}(2,p)$ in the non-Frattini chief factors of finite groups},
  author = {Duong Hoang Dung},
  journal= {arXiv preprint arXiv:1502.05080},
  year   = {2015}
}

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