Cancellation and absorption of lexicographic powers of totally ordered Abelian groups
type: Item
instance of: scholarly article
title: Cancellation and absorption of lexicographic powers of totally ordered Abelian groups
zbMATH Open document ID: 0664.06013
DOI: 10.1007/BF00354895
author: Michèle Giraudet
published in: Order
publication date: 1988-01-01T00:00:00Z
review text: Let G and H be totally ordered Abelian groups such that for some integer k, the lexicographic powers \(G^ k\) and \(H^ k\) are isomorphic (as ordered groups). It was proved by \textit{F. Oger} [Bull. Lond. Math. Soc. 20, 198-202 (1988; Zbl 0619.06012)] that G and H in general need not be isomorphic. The author provides an interesting general technique which shows that G and H are isomorphic whenever G is either divisible or \(\omega_ 1\)-saturated (and in a few more cases); morevoer, G and H are always isomorphic as chains and elementarily equivalent as ordered groups (this latter fact has also been proved by F. Delon and F. Lucas).
reviewed by: Manfred Droste
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 03C60
zbMATH DE Number: 4085728
zbMATH Keywords: elementary equivalence
zbMATH Keywords: totally ordered Abelian groups
zbMATH Keywords: lexicographic powers
MaRDI profile type: Publication
cites work: The elementary theory of abelian groups
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cites work: Q3949052
description: scientific article; zbMATH DE number 4085728