Recognition By Prime Graph of the Almost Simple Group Pgl(2, 25)

Throughout this paper, every groups are finite. the prime graph of a group g is denoted by γ(g). also g is called recognizable by prime graph if for every finite group h with γ(h) = γ(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,p^k) is recognizable by prime graph. so if k is even, the recognition by prime graph of pgl(2,p^k), 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.