论文标题
Adian-Rabin定理 - 英文翻译
The Adian-Rabin Theorem -- An English translation
论文作者
论文摘要
这是Sergei Ivanovich Adian（1931---2020）最初用俄语撰写的四篇非凡文章的英文翻译，并补充了Andrei Andrei Andree Andreevich Markov Jr（1903---1979）的两篇紧密相关文章的翻译。所有六篇文章都涉及各组和单体问题的各种问题的算法不可证明。 S. I. Adian的文章给出了他著名的“ Adian-Rabin定理”的证明，该文章表明，没有算法将算法与“ Markov”属性$ p $一起输入有限的呈现，例如，是琐碎的集团，无限的群体，是无限的等等），以及是否输出了现在是否输出了本财产的财产$ P $。 A. A. Markov（JR）的文章给出了类似于单体的类似结果（结果明显更容易），并出现在组理论类似物之前的几年。详细介绍文章内容和一些评论的序言，包括决定Adian的四篇文章中的哪一篇艰巨的任务应将其视为包含“ Adian-Rabin定理的“”证明。
This is an English translation of four remarkable articles, originally written in Russian, by Sergei Ivanovich Adian (1931--2020), supplemented by the translation of two closely related articles by Andrei Andreevich Markov Jr (1903--1979). All six articles concern algorithmic undecidability of various problems for groups and monoids. The articles by S. I. Adian give his proof of the famous "Adian-Rabin Theorem", which shows that there is no algorithm which takes as input a finite presentation of a group together with a "Markov" property $P$ (e.g. being the trivial group, being infinite, etc.), and which outputs whether or not the presented group has property $P$. The articles by A. A. Markov (Jr) give the analogous result for monoids (a significantly easier result), and appeared several years before the group-theoretic analogue. A preface detailing the contents of the articles and some commentary is provided, including the somewhat difficult task of deciding which of Adian's four articles should be considered as containing "the" proof of the Adian-Rabin theorem.
