论文标题
在$ C_N \ rtimes_s c_2 $上的直接和反向零和逆问题上
On the direct and inverse zero-sum problems over $C_n \rtimes_s C_2$
论文作者
论文摘要
令$ c_n $为订单$ n $的环状组。在本文中，我们提供了$ C_N \ rtimes_s c_2 $的某些零和零常数的确切值，其中$ s \ not \ equiv \ equiv \ equiv \ pm1 \ pmod n $，即$η$ - constant，gao constand，gao constand和erdős-ginzburg-ziv constants constants constants constant and belld's belly a bessy a sille's belle''belle'silld's belle''）结果，我们证明了Gao和Zhuang-Gao对这种形式的群体的猜想。我们还通过表征$ c_n \ rtimes_s c_2 $最大长度的产品结构来解决相关的反问题。
Let $C_n$ be the cyclic group of order $n$. In this paper, we provide the exact values of some zero-sum constants over $C_n \rtimes_s C_2$ where $s \not\equiv \pm1 \pmod n$, namely $η$-constant, Gao constant, and Erdős-Ginzburg-Ziv constant (the latter for all but a "small" family of cases). As a consequence, we prove the Gao's and Zhuang-Gao's Conjectures for groups of this form. We also solve the associated inverse problems by characterizing the structure of product-one free sequences over $C_n \rtimes_s C_2$ of maximum length.
