A finite group G is said to be a Bn-group if any n-element subset A={a1,a2,...,an}of G satisfies∣∣A^2∣∣=|{aiaj|1≤i,j≤n}|≤n(n+1)/2.In this paper,the characterizations of the B6-and B7-groups are given.
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.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5...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.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5,k)groups for 15≤k≤19 have been investigated by several authors.In this paper,we give a complete characterization of B(5,20)2-groups by showing there are five classes of such groups which are nontrivial and nonabelian.展开更多
基金The second author acknowledges the support of the Jiangsu University(Grant No.5501190011).
文摘A finite group G is said to be a Bn-group if any n-element subset A={a1,a2,...,an}of G satisfies∣∣A^2∣∣=|{aiaj|1≤i,j≤n}|≤n(n+1)/2.In this paper,the characterizations of the B6-and B7-groups are given.
文摘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.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5,k)groups for 15≤k≤19 have been investigated by several authors.In this paper,we give a complete characterization of B(5,20)2-groups by showing there are five classes of such groups which are nontrivial and nonabelian.
