A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS

Abstract For any group G, denote by πe(G) the set of orders of elements in G. Given a finite group G, let h(πe(G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G))= k