Hokkaido Mathematical Journal

HIRAMINE Yutaka,

On non-symmetric relative difference sets.

Hokkaido Mathematical Journal, 37 (2008) pp.427-435

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Abstract

Let D be a (m, u, k, λ)-difference set in a group G relative to a subgroup U of G. We say D is symmetric if D^(−1) is also a (m, u, k, λ)-difference set. By a result of [7] D is symmetric if U is a normal subgroup of G. In general, D is non-symmetric when U is not normal in G. In this paper we study a condition under which D is symmetric and show that if D is semiregular then D is symmetric if and only if the dual of dev(D) is a divisible design. We also give a modification of Davis' product construction of relative difference sets and as an application we give a class of non-symmetric semiregular relative difference sets.

MSC(Primary)05B10
MSC(Secondary)
Uncontrolled Keywordsrelative difference set, non-symmetric transversal designs.