Let G be a finite group and d a positive integer.Let s_(dN)(G)denote the smallest positive integer l such that every sequence over G of length at least l contains a nonempty product-one subsequence T with|T|≡0(mod d)...Let G be a finite group and d a positive integer.Let s_(dN)(G)denote the smallest positive integer l such that every sequence over G of length at least l contains a nonempty product-one subsequence T with|T|≡0(mod d).This paper studies s_(dN)(D_(2n))for the dihedral group D_(2n) and shows that when n=2^(r) with r≥3,the equality s_(dN)(D_(2n))=lcm(n,d)+gcd(n,d)holds.展开更多
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite group and d a positive integer.Let s_(dN)(G)denote the smallest positive integer l such that every sequence over G of length at least l contains a nonempty product-one subsequence T with|T|≡0(mod d).This paper studies s_(dN)(D_(2n))for the dihedral group D_(2n) and shows that when n=2^(r) with r≥3,the equality s_(dN)(D_(2n))=lcm(n,d)+gcd(n,d)holds.
