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
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.
