The subword reversing method

TL;DR

The paper reviews the subword reversing method, a semigroup theory technique for constructing diagrams and analyzing algebraic structures, highlighting its effectiveness in solving the word problem and establishing properties of monoids and groups.

Contribution

It summarizes key results of subword reversing, emphasizing its applications in determining cancellativity, embeddability, and solving the word problem in monoids and groups.

Findings

Provides criteria for cancellativity and embeddability.

Offers efficient solutions for the word problem.

Enhances understanding of semigroup structures.

Abstract

We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating presented (semi)groups. In particular, it leads to cancellativity and embeddability criteria for monoids and to efficient solutions for the word problem of monoids and groups of fractions.