The closure of a lattice-ordered permutation group
type: Item
instance of: scholarly article
title: The closure of a lattice-ordered permutation group
zbMATH Open document ID: 0902.06030
author: Richard N. Ball
author: Stephen H. McCleary
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: Let \(\Omega \) be a chain, \(\overline {\Omega }\) its Dedekind completion, and \((G,\Omega)\) a lattice-ordered permutation group (an \(l\)-permutation group). The authors study some completions of \((G,\Omega)\) in the automorphism group \(A(\overline {\Omega })\). For example, they investigate the gate completion consisting of the elements of \(A(\overline {\Omega })\) which can be gated by elements of \(G\), or equivalently, which respect the tyings of \((G,\Omega)\). The results of the paper illuminate several of the standard completions of abstract completely distributive \(l\)-groups using the structure theory of \(l\)-permutation groups.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 1226209
zbMATH Keywords: lattice-ordered group
zbMATH Keywords: \(\alpha \)-completion
zbMATH Keywords: ordered permutation group
zbMATH Keywords: gate completion
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s000120050022
OpenAlex ID: W2061262840
DOI: 10.1007/S000120050022
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description: scientific article; zbMATH DE number 1226209