Elementary theory of free non-abelian groups.
type: Item
instance of: scholarly article
title: Elementary theory of free non-abelian groups.
zbMATH Open document ID: 1110.03020
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: For a group \(G,\) the elementary theory \(\text{Th}(G)\) of \(G\) is the set of all first-order sentences in the language of group theory which are true in \(G.\) Around 1945 Tarski formulated two conjectures about the elementary theory of a free group. The first of them states that the elementary theory of non-abelian free groups of different ranks coincide; the second one states that the elementary theory of free groups is decidable. The scope of this paper is to prove these two conjectures.
Mathematics Subject Classification ID: 03C65
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20A15
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 5078136
zbMATH Keywords: free group
zbMATH Keywords: elementary theory
zbMATH Keywords: decidable theory
author: Olga Kharlampovich
author: Alexei Myasnikov
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.03.033
OpenAlex ID: W2005047182
Wikidata QID: Q55921778
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DOI: 10.1016/J.JALGEBRA.2006.03.033
description: scientific article; zbMATH DE number 5078136