Representations of free lattice-ordered groups
type: Item
instance of: scholarly article
title: Representations of free lattice-ordered groups
zbMATH Open document ID: 0803.06017
DOI: 10.1007/BF01108831
published in: Order
publication date: 1995-01-03T00:00:00Z
review text: Let \(\eta\) be any uncountable cardinal, \(G_ \eta\) be the free group and \(F_ \eta\) be the free lattice-ordered group of rank \(\eta\). The author shows that there exists a right ordering of \(G_ \eta\) on which the natural action of \(F_ \eta\) is both faithful and pathologically 2- transitive. Furthermore, he describes the structure of the root system of prime subgroups of \(F_ \eta\). The results obtained generalize analogous ones by \textit{S. H. McCleary} [Trans. Am. Math. Soc. 290, 81-100 (1985; Zbl 0546.06013)], where the generalized continuum hypothesis and regularity of \(\eta\) have been required.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 549275
zbMATH Keywords: ordered permutation group
zbMATH Keywords: free group
zbMATH Keywords: free lattice-ordered group
zbMATH Keywords: right ordering
zbMATH Keywords: root system of prime subgroups
author: Manfred Droste
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
cites work: Q3752440
cites work: Free lattice-ordered groups
cites work: The root system of prime subgroups of a free lattice-ordered group (without G.C.H.)
cites work: Q4168953
cites work: Free Lattice-Ordered Groups Represented as o-2 Transitive l-Permutation Groups
cites work: An Even Better Representation for Free Lattice-Ordered Groups
cites work: Q3949052
description: scientific article; zbMATH DE number 549275