Periodic ordered permutation groups and cyclic orderings
type: Item
instance of: scholarly article
title: Periodic ordered permutation groups and cyclic orderings
zbMATH Open document ID: 0821.20001
author: Dugald Macpherson
author: Manfred Droste
author: Michèle Giraudet
published in: Journal of Combinatorial Theory. Series B
publication date: 1995-07-02T00:00:00Z
review text: It is shown that periodic ordered permutation groups satisfying certain extra conditions are very nearly simple. This is applied to several natural examples, such as the following. (i) If \(z\) denotes the map \(x \mapsto x + 1\) on \(\mathbb{R}\), and \(\text{Diff}(\mathbb{R})\) is the group of diffeomorphisms of \(\mathbb{R}\), then \(C_{\text{Diff}(\mathbb{R})}(\langle z \rangle)/\langle z \rangle\) is simple. (ii) The automorphism group of the countable homogeneous local order (one of the three countable homogeneous tournaments) is simple. Also, an extension of Rieger's Theorem is given, relating groups of automorphisms of cyclic orderings to groups of automorphisms of total orderings.
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 20B07
zbMATH DE Number: 767697
zbMATH Keywords: periodic ordered permutation groups
zbMATH Keywords: groups of diffeomorphisms
zbMATH Keywords: automorphism groups
zbMATH Keywords: countable homogeneous local orders
zbMATH Keywords: countable homogeneous tournaments
zbMATH Keywords: cyclic orderings
zbMATH Keywords: groups of automorphisms
zbMATH Keywords: total orderings
Wikidata QID: Q56269723
reviewed by: Manfred Droste
MaRDI profile type: Publication
full work available at URL: jctb.1995.1022
OpenAlex ID: W2116408734
DBLP publication ID: journals/jct/DrosteGM95
DOI: 10.1006/JCTB.1995.1022
description: scientific article; zbMATH DE number 767697