一类亚循环群的Harborth常数
Harborth Constants for Certain Classes of Metacyclic Groups
摘要：
有限群$G$的哈波斯常数是最小整数$k\geq \exp(G)$，使得大小为$k$的$G$的任何子集包含$\exp(G)$不同的元素，其乘积是$1$。推广了以前关于二面体群的Harborth常数的工作，我们计算了$H_{n, m}=\langle x, y \mid x^n=1, y^2=x^m, yx=x^{-1}y \rangle$形式的亚循环群的Harborth常数。我们还解决了“逆”的问题，表征所有较小的子集，不包含$\exp(H_{n,m})$不同的元素，其产品是$1$。
英文摘要：
The Harborth constant of a finite group $G$ is the smallest integer $k\geq \exp(G)$ such that any subset of $G$ of size $k$ contains $\exp(G)$ distinct elements whose product is $1$. Generalizing previous work on the Harborth constants of dihedral groups, we compute the Harborth constants for the metacyclic groups of the form $H_{n, m}=\langle x, y \mid x^n=1, y^2=x^m, yx=x^{-1}y \rangle$. We also solve the "inverse" problem of characterizing all smaller subsets that do not contain $\exp(H_{n,m})$ distinct elements whose product is $1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
