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\end{document} − 1). There are further constraints on n, a and ∈. We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, λ) difference set D and has a dihedral image D2m with either (n, m) = 1 or m = pt for p an odd prime dividing n, then one of the C2 intersection numbers of D is divisible by m. Again, this gives some non-existence results.
