Reversional automorphisms of lattice-ordered groups
type: Item
instance of: scholarly article
title: Reversional automorphisms of lattice-ordered groups
zbMATH Open document ID: 0856.06010
DOI: 10.1007/BF02107323
author: N. V. Bayanova
author: O. V. Nikonova
published in: Siberian Mathematical Journal
publication date: 1997-02-24T00:00:00Z
review text: A group automorphism \(\varphi\) of an \(\ell\)-group \(G\) is said to be reversional if \(x\leq y\) implies \(\varphi x\geq \varphi y\) for all \(x, y\in G\). Evidently, every finite-order reversional automorphism of an \(\ell\)-group has order 2. Since \(\varphi^2= 1\), it follows that \(\varphi= \varphi^{- 1}\). The authors prove the following: Let \(G\) be a totally ordered group and let \(A\) be a totally ordered Abelian group. The group \(\text{Awr}G\) with ordering of type (A) or (B) possesses no reversional automorphism. Therefore a totally ordered group is isomorphically embeddable into a totally ordered group without reversional automorphisms.
reviewed by: František Šik
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20F60
zbMATH DE Number: 923534
zbMATH Keywords: lattice-ordered groups
zbMATH Keywords: wreath product
zbMATH Keywords: group automorphism
zbMATH Keywords: reversional automorphism
zbMATH Keywords: totally ordered group
MaRDI profile type: Publication
cites work: Groupes à moitié ordonnés
cites work: Q3682535
cites work: Q4745979
cites work: On reversing the order of a lattice ordered group
description: scientific article; zbMATH DE number 923534