Od-Characterization of Almost Simple Groups Related to L2(49) (original) (raw)

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L2(49). As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L2(49) except L2(49)· 2 2 . Also, we prove that if M is an almost simple group related to L2(49) except L2(49)· 2 2 and G is a finite group such that|G| =|M| and ( G) = ( M), then G = M. Throughout this paper, groups under consideration are finite. For any group G, we denote by e(G) the set of orders of its elements and by (G) the set of prime divisors of |G|. We associate to (G) a simple graph called prime graph of G, denoted by ( G). The vertex set of this graph is (G), and two distinct vertices p, q are joined by an edge if and only if pq 2 e(G). In this case, we write p q. Denote by t(G) the number of connected components of ( G) and by i = i(G) (i = 1, 2,...,t(G)) the co...