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August 2008 On non-symmetric relative difference sets
Yutaka HIRAMINE
Hokkaido Math. J. 37(3): 427-435 (August 2008). DOI: 10.14492/hokmj/1253539528

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.

Citation

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Yutaka HIRAMINE. "On non-symmetric relative difference sets." Hokkaido Math. J. 37 (3) 427 - 435, August 2008. https://doi.org/10.14492/hokmj/1253539528

Information

Published: August 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1176.05014
MathSciNet: MR2441910
Digital Object Identifier: 10.14492/hokmj/1253539528

Subjects:
Primary: 05B10

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 3 • August 2008
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