A characterization of the symmetric group of prime degree

Document Type : Research Paper


School of Sciences, Nantong University, 226007, Nantong, P. R. China


Let $G$ be a finite group and $\Gamma(G)$ the prime graph of $G$‎. ‎Recently people have been using prime graphs to study simple groups‎. ‎Naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? In this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$G\cong S_p$ if and only‎ ‎if $|G|=|S_p|$ and $\Gamma(G)=\Gamma(S_p)$‎, ‎where $p$ is a prime‎.


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