On subsets of partial difference sets
A \((v, k, \lambda, \mu)\)-partial difference set \(D\) is a \(k\)-subset of an abelian group \(G\) of order \(v\) such that \(-D = D\) and the list of differences \(d - d'\) (\(d, d'\in D, d \neq d'\)) contains every nonidentity element in \(D\) exactly \(\lambda\) times and the nonidentity elements not in \(D\) exactly \(\mu\) times. Partial difference sets are a generalization of difference sets with multiplier \(-1\). Extending a result of \textit{R. L. McFarland} [J. Comb. Theory, Ser. A 54, No. 1, 112-122 (1990; Zbl 0728.05012)] the author shows that \(D \cap H\) is a partial difference set in \(H\) if the order of \(H\) and its index in \(G\) are coprime and the index of \(H\) is odd. Some nonexistence results on partial difference sets follow from this theorem.
scientific article; zbMATH DE number 562670