Orders of units in integral group rings and blocks of defect 1

We show that if a Sylow p-subgroup of a finite group G is of order p, then the normalized unit group of the integral group ring of G contains a normalized unit of order pq if and only if G contains an element of order pq, where q is any prime. We use this result to answer the Prime Graph Question for most sporadic simple groups and some simple groups of Lie type, including seven new infinite series' of such groups. Our methods are based on understanding of blocks of cyclic defect and Young tableaux combinatorics.