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.