Dillon has conjectured that any group of order 22d+2 with a normal subgroup isomorphic to Z2d+1 will have a difference set. He was able to show that this is true if the subgroup is central: this paper extends that idea to noncentral subgroups.
Copyright © 1991, Elsevier. This article first appeared in Journal of Combinatorial Theory, Series A: 57:2 (1991), 238-242.
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Davis, James A. "A Result on Dillon's Conjecture in Difference Sets." Journal of Combinatorial Theory, Series A 57, no. 2 (July 1991): 238-42. doi:10.1016/0097-3165(91)90047-K.