Relative difference sets fixed by inversion (III)—Cocycle theoretical approach Original Research Article

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 image of G such that image and image for all image. 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.