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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].

##### MSC:
 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
##### Keywords:
difference set; divisible designs