The perfect order subset conjecture for simple groups

This paper verifies the Perfect Order Subset Conjecture for Simple Groups for all but one family of finite simple groups. Specifically, for each nonabelian finite simple group G there is some N such that the cardinality of the nonempty subset of all elements of order N in G does not divide the order of G, unless G is an orthogonal group of plus type in dimension 4n, for some n⩾2.