论文标题
有效可分离性的调查
Survey on effective separability
论文作者
论文摘要
分组的可分离性是指在有限的商中可以检测到的一个组的哪个子集。从经典上讲，可以根据哪些类具有一定的可分离性属性来研究可分离性，并且这个问题与诸如“问题”一词之类的组中的算法问题有关。最新的观点试图研究最小有限商的顺序，其中人们根据其复杂性检测到的子集，该子集在有限生成的群体上使用规范来测量。在这项调查中，我们介绍了当前在有效的可分离性领域中所知的内容，并概述了几类小组的开放问题。
Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is related to algorithmic problems in groups such as the word problem. A more recent perspective tries to study the order of the smallest finite quotient in which one detects the subset under consideration depending on its complexity, measured using the word norm on a finitely generated group. In this survey, we present what is currently known in the field of effective separability and give an overview of the open questions for several classes of groups.
