Abstract: | Partial difference sets with parameters (,k,,µ) = (,( 1)/2, ( 5)/4,( 1)/4) are called Paleypartial difference sets. By using finite local rings, we constructa family of Paley PDSs for abelian p-groups with any given exponent.Furthermore, we prove some non-existence results on Paley PDSs.Using these results, we prove that Paley PDSs exist in a rank2 abelian group if and only if the group is isomorphic to Zpr x Zp r where p is an odd prime. |