In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i={a 1,a 2,…,a m} and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i={b 1,b 2,…,b k};(3)...In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i={a 1,a 2,…,a m} and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i={b 1,b 2,…,b k};(3) ∩ni=1A 1{b 1,b 2,…,b k}; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.展开更多
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In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i={a 1,a 2,…,a m} and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i={b 1,b 2,…,b k};(3) ∩ni=1A 1{b 1,b 2,…,b k}; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.
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.