Partial difference sets in \(p\)-groups (Q1337784)

Partial difference sets (PDSs) have been constructed in elementary abelian \(p\)-groups. Several authors have inquired about the existence of PDSs with the same parameters in other (non-elementary) abelian \(p\)- groups. This paper provides an exponent bound for PDSs in abelian \(p\)- groups for the Paley parameters. We also provide the first construction of a PDS with the Paley parameters in a nonelementary abelian group. We note the implications to reversible divisible difference sets.