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Difference sets in noncyclic Abelian groups. (English) Zbl 0748.05028
Let G be an additive Abelian group of order v. A (v,k,λ)- difference set in G is the set D of k elements of G such that any non-zero element gG has λ representations in the form g=d 1 -d 2 , where d 1 , d 2 are two elements of D. The existence of (v,k,λ)-difference sets in non-cyclic Abelian groups was yet studied for k50 by E. S. Lander. This paper continues this investigation for k100. 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:
05B10Difference sets
20D60Arithmetic and combinatorial problems on finite groups