McFarland's conjecture on abelian difference sets with multiplier −1

This paper is a continuation of the work by R.L. McFarland and S.L. Ma on abelian difference sets with −1 as a multiplier. More nonexistence results are obtained as a consequence of a theorem on the existence of sub-difference sets. In particular, nonexistence is shown for the two cases left undecided by McFarland and Ma.