Difference Sets Disjoint from a Subgroup II: Groups of Order $$4p^2$$

Abstract

We study finite groups G having a normal subgroup H and \(D \subset G \setminus H, D \cap D^{-1}=\emptyset ,\) such that the multiset \(\{ xy^{-1}:x,y \in D\}\) has every non-identity element occur the same number of times (such a D is called a DRAD difference set). We show that there are no such groups of order \(4p^2\), where p is an odd prime.