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.
The first author is a faculty member of Philippine Normal University (PNU), Manila on study leave at Kumamoto University under a Monbusho grant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Davis, J.A., Jedwab, J., Mowbray, M.: New Famihes of Semi-Regular Relative Difference Sets. Designs, Codes and Cryptography 13 (1998) 131–146
Ito, N.: On Hadamard groups. J. of Algebra 168 (1994) 981–987
Pott, A.: Finite Geometry and Character Theory. Lecture Notes in Mathematics 1601, Springer-Verlag, Berlin (1995)
Schmidt, B.: On (p a, p b, p a, p a−b) Relative Difference Sets. J. Algebraic Combin. 6 (1997) 279–297
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Elvira, D., Hiramine, Y. (2001). On Non-Abelian Semi-Regular Relative Difference Sets. In: Jungnickel, D., Niederreiter, H. (eds) Finite Fields and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56755-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-56755-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62498-8
Online ISBN: 978-3-642-56755-1
eBook Packages: Springer Book Archive