论文标题
群体自动形态的决定因素
A determinant for automorphisms of groups
论文作者
论文摘要
令$ h $和$ k $为组。在本文中，我们介绍了$ h \ times k $的自动形态的决定因素的概念，以及组对的一些不兼容概念，以衡量$ h $和$ k $的量度，这是同构的票价。借助这些定义从这些定义开发的工具，我们通过其决定因素来表征$ h \ times k $的可逆自动形态，并明确描述AUT（$ h \ times k $）作为一组$ 2 $ by-by-by-2 $矩阵的矩阵，如果是$ h $ h $ h $ h $或$ k $，则属于某些相关类别的类别。将介绍决定因素的许多理论和实际应用，以及示例以及对决定因素的某些计算优势的分析。
Let $H$ and $K$ be groups. In this paper we introduce a concept of determinant for automorphisms of $H\times K$ and some concepts of incompatibility for group pairs as a measure of how much $H$ and $K$ are fare from being isomorphic. With the aid of the tools developed from these definitions, we give a characterisation of invertible automorphisms of $H\times K$ by means of their determinants and an explicit description of Aut($H\times K$) as a group of $2$-by-$2$ matrices, in case $H$ or $K$ belong to some relevant classes of groups. Many theoretical and practical applications of the determinants will be presented, together with examples and an analysis on some computational advantages of the determinants.
