Let G be a group of order mn and N a subgroup of G of order n. If D is a k-subset of G, then D is called a (m, n, k, λ1, λ2) divisible difference set (DDS) provided that the differences dd'-1 for d, d'D, d ≠ d' contain every nonidentity element of N exactly λ1 times and every element of G - N exactly λ2 times. Difference sets are used to generate designs, as described by [4] and [9]. D will be called an Almost Difference set (ADS) if λ1 and λ2 differ by 1. The reason why these are interesting involves their relationship to symmetric difference sets. A symmetric difference set is a DDS with λ1 = λ2, so the ADS are "almost" difference sets. Symmetric difference sets are becoming more and more difficult to construct, and this is as close as we can get with a divisible difference set.

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Copyright © 1992, Birkhäuser-Verlag. This article first appeared in Archiv der Mathematik: 59:6 (1992), 595-602.
