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A finite group G is said to be a B(n, k) group if |{aiaj|1≤i,j≤n}|≤k for any n-element subset {a1,…,an} of G. The aim of this paper is to give a characterization of the B(5, 19) non-2-group...

A finite group G is said to be a B(n, k) group if for any n-element subset {a 1,…, a n } of G, |{a i a j |1 ≤ i, j ≤ n}| ≤k. In this article, we give characterizations of the B(5, 19) 2-groups, and the B(6, k) 2-groups for 21 ≤ k ≤ 28.

A group G is said to be a B(n, k) group if for any n-element subset {a 1,…, a n } of G, |{a i a j | 1 ≤ i, j ≤ n}| ≤k. In this article, we give a complete characterization of B(4, 13) 2-groups, and then obtain a complete characterization of B(4, 13) groups.

A group G is said to be a B(n,k) group if for any n-element subset {a1,…, an} of G, |{aiaj | 1≤i, j≤n}|≤ k. In this paper, characterizations of B(4,11) groups, B(4,12) groups, and B(4,13) non-2-groups are given.