Erratum to "Generalized Relative Difference Sets"

Lam, Clement; Payne, Sam

doi:10.2307/2041646

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Cited by 3 publications

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“…The only examples of RDS's with the parameters of Theorem 6.4 known to us are cyclic (7, 2, 4, 1) --and (31, 2, 16, 4) -RDS's, see Lain [22]. Since n = 2, here, these examples of course do not admit 2 as a multiplier.…”

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confidence: 91%

Some non-existence results on divisible difference sets

et al. 1991

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In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches:(i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets, (ii) involution arguments and (iii) multipliers in conjunction with results on ordinary difference sets.Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd order n.

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confidence: 91%