New families of semi-regular relative difference sets
Attention to the character sum of subsets of an abelian group helps to set many constructions for relative difference sets such that \(k=n\lambda\) (where \(n\) is the order of the ``forbidden'' group). The cases in which \(n\) is a power of \(2\) and in which \(n=3\) are developed obtaining very new relative difference sets also in groups whose order is not a prime power and even can contain more than two distinct prime factors. Contracting, direct products, recursive and combinatorial constructions are used and combined also suggesting similar explorations for other cases to solve open problems given to the end.
scientific article; zbMATH DE number 1115729