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Asymptotic nonexistence of difference sets in dihedral groups. (English) Zbl 1002.05006
Summary: We prove that for any primes $p_1,\dots, p_s$ there are only finitely many numbers $\prod^s_{i=1} p^{\alpha_i}_i$, $\alpha_i\in \bbfZ^+$, which can be orders of dihedral difference sets. We show that, with the possible exception of $n= 540,225$, there is no difference set of order $n$ with $1< n\le 10^6$ in any dihedral group.

MSC:
 05B10 Difference sets
Keywords:
dihedral difference sets
Full Text:
References:
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