Groups With the Same Prime Graph as an Almost Sporadic Simple Group

Abstract: Let $G$ be a finite group. We denote by $\Gamma(G)$ the prime graph of $G$. Let $S$ be a sporadic simple group. M. Hagie in (Hagie, M. (2003), The prime graph of a sporadic simple group, Comm. Algebra, 31: 4405-4424) determined finite groups $G$ satisfying $\Gamma(G)=\Gamma(S)$. In this paper we determine finite groups $G$ such that $\Gamma(G)=\Gamma(A)$ where $A$ is an almost sporadic simple group, except $\Aut (McL)$ and $\Aut (J_2)$.

Keywords: Almost sporadic simple groups, prime graph, order elements

Classification (MSC2000): 20D05; 20D60, 20D08

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