Group theory via global semigroup theory
type: Item
instance of: scholarly article
title: Group theory via global semigroup theory
zbMATH Open document ID: 0668.20048
DOI: 10.1016/0021-8693(89)90199-3
author: J.-C. Birget
author: John L. Rhodes
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Groups are shown to be special homomorphic images of residually finite inverse semigroups. To this aim the authors define three types of expansions of semigroups. When the starting semigroup is a group the three types of expansions give isomorphic semigroups and (selecting a large enough generator set for the group) the expansion thus obtained is an inverse semigroup. The results are applied to the Burnside problem and the following proposition is obtained: Let G be a finite group of odd order. Then G is a homomorphic image of a bounded torsion semigroup the finite subgroups of which are cyclic.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4093769
zbMATH Keywords: residually finite inverse semigroups
zbMATH Keywords: expansions of semigroups
zbMATH Keywords: generator set
zbMATH Keywords: Burnside problem
zbMATH Keywords: finite group of odd order
reviewed by: Tero Harju
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90199-3
OpenAlex ID: W2051124363
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cites work: Q3337662
cites work: New estimates of odd exponents of infinite Burnside groups.
description: scientific article; zbMATH DE number 4093769