On Non-Abelian Semi-Regular Relative Difference Sets

Dominic Elvira and Yutaka Hiramine
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Dominic Elvira: Kumamoto University, Department of Mathematics Graduate School of Science and Technology
Yutaka Hiramine: Kumamoto University, Department of Mathematics Faculty of Education

A chapter in Finite Fields and Applications, 2001, pp 122-127 from Springer

Abstract: Abstract In their paper [1] J.A. Davis, J. Jedwab and M. Mowbray gave new constructions of abelian semi-regular RDS’s by using (k, m, t)-building sets on abelian groups. In this article, we generalize this concept by defining a t-building set, a certain collection of elements from a group ring. We then study t-building sets on cyclic p-groups and apply our results to show that there is no non-trivial semi-regular RDS in any dihedral group. We also show that for any dicyclic group, its forbidden subgroup of even order is isomorphic to ℤ2.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56755-1_12

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DOI: 10.1007/978-3-642-56755-1_12

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