Solvable word problems in semigroups
type: Item
instance of: scholarly article
title: Solvable word problems in semigroups
zbMATH Open document ID: 0821.20040
DOI: 10.1007/BF02573520
author: V. Pereyra
published in: Semigroup Forum
publication date: 1995-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/135382
review text: A semigroup \(S\) with presentation \((X;R)\) is a \(C(n)\) semigroup \((n \geq 1)\) if no \(R\)-word is a product of fewer than \(n\) pieces (a piece being a word which is a common factor of \(R\)-words in at least two distinct ways). Every finitely presented \(C(n)\) semigroup has a solvable word problem for all \(n \geq 3\) (for background and details see the reviewer's book `Techniques of Semigroup Theory' [Oxf. Univ. Press, 1982; Zbl 0744.20046]). In this paper the analogy with the small cancellation theory of groups is completed by showing that \(S\) has a solvable word problem if \(S\) is finitely presented and the presentation satisfies \(C(2)\) and \(T(4)\), where \(T(4)\) is a condition which forbids the occurrence of four particular subgraphs in the so-called star graph of the presentation.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20F06
zbMATH DE Number: 736957
zbMATH Keywords: presentations
zbMATH Keywords: \(C(n)\) semigroups
zbMATH Keywords: solvable word problem
zbMATH Keywords: small cancellation theory
zbMATH Keywords: finitely presented semigroups
zbMATH Keywords: star graphs
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
cites work: Q4003180
cites work: On the T(q)-conditions of small cancellation theory
cites work: Q4145882
OpenAlex ID: W2080424867
description: scientific article; zbMATH DE number 736957