zbMATH — the first resource for mathematics

A survey on relative difference sets. (English) Zbl 0847.05018
Arasu, K. T. (ed.) et al., Groups, difference sets, and the Monster. Proceedings of a special research quarter, Columbus, OH, USA, Spring 1993. Berlin: Walter de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 4, 195-232 (1996).
A relative difference set with parameters \((m, n, k, \lambda)\) is a \(k\)-subset \(R\) in a group \(G\) of order \(mn\) relative to a normal subgroup \(N\) of order \(n\) such that the list of differences \(r - s\) \((r, s \in R\), \(r \neq s)\) contains no element of \(N\) and contains each element of \(G \setminus N\) exactly \(\lambda\) times. Such objects generalize ordinary difference sets (the case \(n =1\)) and belong to symmetric divisible designs admitting \(G\) as a regular automorphism group. The author gives a useful and very well-written survey on relative difference sets.
For the entire collection see [Zbl 0836.00028].

05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)