The word problem for one-relation monoids: a survey
The word problem for one-relation monoids: a survey
复制标题
单关系幺半群的文字问题：一项调查
作者：
Carl
本文旨在概述组合代数中最古老和最著名的开放问题之一：单关系一元群的字问题。我们提供了从1914年开始的这个问题的历史，并给出了中心结果的证明的详细概述，特别是由于Adian和他的学生Oganesian。在展示了如何将问题减少到左边的取消案例之后，调查的第二部分侧重于解决这个家庭部分案例的各种方法。我们以一些与这个问题有关的现代和最近的结果结束，包括与科拉茨猜想的联系。在此过程中，我们强调并解决了多年来文献中出现的一些不正确和不准确的陈述。我们也填补了一个证明特殊逆模群与单关系模群的定理的空白，并稍微加强了这个定理的陈述。
This survey is intended to provide an overview of one of the oldest and most celebrated open problems in combinatorial algebra: the word problem for one-relation monoids. We provide a history of the problem starting in 1914, and give a detailed overview of the proofs of central results, especially those due to Adian and his student Oganesian. After showing how to reduce the problem to the left cancellative case, the second half of the survey focuses on various methods for solving partial cases in this family. We finish with some modern and very recent results pertaining to this problem, including a link to the Collatz conjecture. Along the way, we emphasise and address a number of incorrect and inaccurate statements that have appeared in the literature over the years. We also fill a gap in the proof of a theorem linking special inverse monoids to one-relation monoids, and slightly strengthen the statement of this theorem.
关于特殊单位和一关系逆幺半群的群
影响因子：
0.9
作者：
Gray R
通讯作者：
Gray R