a Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435-0001, USA b School of Mathematical and Geospatial Science, RMIT-City Campus, GPO Box 2476V, Melbourne, Vic. 3001, Australia
Abstract:
In this paper, we give a characterization of a group G which contains a semiregular relative difference set R relative to a central subgroup N containing the commutator subgroup G,G] of G such that 1∈R and rRr=R for all r∈R. In particular, these relative difference sets are fixed by inversion and inner automorphisms of the group are multipliers. We also present a construction of such relative difference sets.