论文标题
有限群体及其特征的广义亚历山大·普通（Alexander Quandles）
Generalized Alexander quandles of finite groups and their characterizations
论文作者
论文摘要
本文的目的是用基础群体的语言来表征有限群体的广义亚历山大·夸德尔斯（Alexander Quandles）。首先，我们证明，如果有限组$ g $很简单，那么$ g $的广义亚历山大·奎德尔斯（Alexander Quandles of Alexander Quandles）的Quandle同构类别对应于$ g $的自动形态群体的共轭类。对于对称组的情况，也可以要求这种对应关系。其次，根据某些假设，我们对有限群体$ g $的广义亚历山大·奎德尔斯（Alexander Quandles）进行了特征。作为这种表征的推论，我们在某些特定群体中获得了几个特征，例如阿贝尔群体和二面群。最后，我们对订单最高$ 15 $的团体产生的广义亚历山大·夸德尔（Alexander Quandles）进行了特征。
The goal of this paper is to characterization generalized Alexander quandles of finite groups in the language of the underlying groups. Firstly, we prove that if finite groups $G$ are simple, then the quandle isomorphic classes of generalized Alexander quandles of $G$ one-to-one correspond to the conjugacy classes of the automorphism groups of $G$. This correspondence can be also claimed for the case of symmetric groups. Secondly, we give a characterization of generalized Alexander quandles of finite groups $G$ under some assumptions in terms of $G$. As corollaries of this characterization, we obtain several characterizations in some particular groups, e.g., abelian groups and dihedral groups. Finally, we perform a characterization of generalized Alexander quandles arising from groups with their order up to $15$.
