Abstract
It is known that if G is a group of order 4 N 2, and G contains N mutually disjoint subgroups of order 2 N, then the nonidentity elements of these subgroups form a difference set in G. Gluck recently discovered a nonabelian example with N = 4 and showed it to be the only case with N = 4 and G not elementary abelian. We show here that the only examples with N > 4 are elementary abelian 2-groups.
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