Elementary theory of free non-abelian groups

Olga Kharlampovich; Alexei Myasnikov

doi:10.1016/j.jalgebra.2006.03.033

Elementary theory of free non-abelian groups

Olga Kharlampovich
, Alexei Myasnikov

Department of Mathematical Sciences

McGill University

Research output: Contribution to journal › Article › peer-review

183 Scopus citations

Abstract

We prove that any two non-abelian free groups have the same elementary theory and that this theory is decidable. These results solve two questions that were raised by Tarski in 1945.

Original language	English
Pages (from-to)	451-552
Number of pages	102
Journal	Journal of Algebra
Volume	302
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.03.033
State	Published - 15 Aug 2006

Keywords

Elementary theory
Free group

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10.1016/j.jalgebra.2006.03.033

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title = "Elementary theory of free non-abelian groups",

abstract = "We prove that any two non-abelian free groups have the same elementary theory and that this theory is decidable. These results solve two questions that were raised by Tarski in 1945.",

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AU - Myasnikov, Alexei

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N2 - We prove that any two non-abelian free groups have the same elementary theory and that this theory is decidable. These results solve two questions that were raised by Tarski in 1945.

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DO - 10.1016/j.jalgebra.2006.03.033

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JO - Journal of Algebra

JF - Journal of Algebra

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Elementary theory of free non-abelian groups

Abstract

Keywords

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