Recognition by prime graph of the almost simple group PGL(2; 25)

Throughout this paper, every groups are nite. The prime graph of a group G is denoted by 􀀀(G). Also G is called recognizable by prime graph if for every nite group H with 􀀀(H) = 􀀀(G), we conclude that G = H. Until now, it is proved that if k is an odd number and p is an odd prime number, then PGL(2; pk) is recognizable by prime graph. So if k is even, the recognition by prime graph of PGL(2; pk), where p is an odd prime number, is an open problem. In this paper, we generalize this result and we prove that the almost simple group PGL(2; 25) is recognizable by prime graph.