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On Non-Abelian Semi-Regular Relative Difference Sets

In: Finite Fields and Applications

Author

Listed:
  • Dominic Elvira

    (Kumamoto University, Department of Mathematics Graduate School of Science and Technology)

  • Yutaka Hiramine

    (Kumamoto University, Department of Mathematics Faculty of Education)

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.

Suggested Citation

  • Dominic Elvira & Yutaka Hiramine, 2001. "On Non-Abelian Semi-Regular Relative Difference Sets," Springer Books, in: Dieter Jungnickel & Harald Niederreiter (ed.), Finite Fields and Applications, pages 122-127, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56755-1_12
    DOI: 10.1007/978-3-642-56755-1_12
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