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Zbl 0748.05028
Kopilovich, L.E.
Difference sets in noncyclic Abelian groups.
(English. Russian original)
[J] Cybernetics 25, No.2, 153-157 (1989); translation from Kibernetika 1989, No.2, 20-23 (1989). ISSN 0011-4235

Let $G$ be an additive Abelian group of order $v$. A $(v,k,\lambda)$- difference set in $G$ is the set $D$ of $k$ elements of $G$ such that any non-zero element $g\in G$ has $\lambda$ representations in the form $g=d\sb 1-d\sb 2$, where $d\sb 1$, $d\sb 2$ are two elements of $D$. The existence of $(v,k,\lambda)$-difference sets in non-cyclic Abelian groups was yet studied for $k\le 50$ by E. S. Lander. This paper continues this investigation for $k\le 100$. Five criteria of non-existence of a difference set are used. The results are listed in a table. In this table still some unsolved cases (denoted by the symbol?) remain.
MSC 2000:
*05B10 Difference sets
20D60 Arithmetic and combinatorial problems on finite groups

Keywords: difference set; Abelian group

Cited in: Zbl 1065.05022

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