Odd Automorphisms of Sylow 2-subgroups of sporadic simple groups.
In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except .
Let be a finite group. The prime graph of is a simple graph whose vertex set is and two distinct vertices and are joined by an edge if and only if has an element of order . A group is called -recognizable by prime graph if there exist exactly nonisomorphic groups satisfying the condition . A 1-recognizable group is usually called a recognizable group. In this problem, it was proved that is recognizable, if is an odd prime and is odd. But for even , only the recognizability...