Title: Davenport constant and its variants for some non-abelian groups Show Chinese title

Title: 达文波特常数及其在某些非阿贝尔群中的变体

Abstract: We define two variants $e(G)$, $f(G)$ of the Davenport constant $d(G)$ of a finite group $G$, that is not necessarily abelian. These naturally arising constants aid in computing $d(G)$ and are of potential independent interest. We compute the constants $d(G)$, $e(G)$, $f(G)$ for some nonabelian groups G, and demonstrate that, unlike abelian groups where these constants are identical, they can each be distinct. As a byproduct of our results, we also obtain some cases of a conjecture of J. Bass. We compute the $k$-th Davenport constant for several classes of groups as well. We also make a conjecture on $f(G)$ for metacyclic groups and provide evidence towards it. Show Chinese abstract

Abstract: 我们定义了有限群$G$的戴维森常数$d(G)$的两个变体$e(G)$,$f(G)$，该有限群不一定为阿贝尔群。 这些自然出现的常数有助于计算$d(G)$，并且可能具有独立的兴趣。 我们计算了一些非交换群G的常数$d(G)$、$e(G)$、$f(G)$，并证明与交换群中这些常数相同的情况不同，它们可以各不相同。 作为我们结果的副产品，我们也得到了J. Bass的一个猜想的一些情况。 我们还计算了几个群类的$k$-阶Davenport常数。 我们还对元循环群的$f(G)$提出了一个猜想，并提供了支持该猜想的证据。