On a class of semigroups with symmetric presentations
type: Item
instance of: scholarly article
title: On a class of semigroups with symmetric presentations
zbMATH Open document ID: 0794.20063
DOI: 10.1007/BF02573573
author: Richard M. Thomas
author: C. M. Campbell
author: E. F. Robertson
published in: Semigroup Forum
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/135237
review text: The authors study semigroups \(S(m,n)\) with the presentations \[ \langle x_ 1,\dots, x_ n:\;x_ i^{m+1}= x_ i,\;x_ i x_ j^ 2= x_ j x_ i^ 2,\;1\leq i,j\leq n\rangle. \] The structure of these semigroups is determined as follows: if \(m\) is odd then \(S(m,n)\) is a semilattice of groups, if \(m\) is even then \(S(m,n)\) is a semilattice of right groups. For those \((m,n)\) for which \(S(m,n)\) is finite, formulas for the cardinality \(| S(m,n)|\) are obtained. For odd \(m\) this is the case iff \((m,3)=1\) or \((m,3)=3\) and \(n\leq 3\); for even \(m\) this happens iff \(m\leq 4\).
reviewed by: K. Auinger
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 164968
zbMATH Keywords: semigroups
zbMATH Keywords: presentations
zbMATH Keywords: semilattice of groups
zbMATH Keywords: semilattice of right groups
MaRDI profile type: Publication
cites work: Coset Enumeration in a Finitely Presented Semigroup
cites work: Some Remarks on Semigroup Presentations
cites work: A practical method for enumerating cosets of a finite abstract group
OpenAlex ID: W2791488526
description: scientific article; zbMATH DE number 164968