2 research outputs found
Semi-regular Relative Difference Sets with Large Forbidden Subgroups
Motivated by a connection between semi-regular relative difference sets and
mutually unbiased bases, we study relative difference sets with parameters
in groups of non-prime-power orders. Let be an odd prime. We
prove that there does not exist a relative difference set in any
group of order , and an abelian relative difference set can
only exist in the group . On the other hand, we
construct a family of non-abelian relative difference sets with parameters
, where is an odd prime power greater than 9 and
(mod 4). When is a prime, , and 1 (mod 4), the
non-abelian relative difference sets constructed here are
genuinely non-abelian in the sense that there does not exist an abelian
relative difference set with the same parameters