Groups elementarily equivalent to a free nilpotent group of finite rank

Alexei G. Myasnikov; Mahmood Sohrabi

doi:10.1016/j.apal.2011.04.003

Groups elementarily equivalent to a free nilpotent group of finite rank

Department of Mathematical Sciences

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

6 Scopus citations

Abstract

In this paper, we give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite rank over an arbitrary binomial domain. In particular, we characterize all groups elementarily equivalent to a free nilpotent group of finite rank.

Original language	English
Pages (from-to)	916-933
Number of pages	18
Journal	Annals of Pure and Applied Logic
Volume	162
Issue number	11
DOIs	https://doi.org/10.1016/j.apal.2011.04.003
State	Published - Nov 2011

Keywords

Abelian deformation
Elementary equivalence
Free nilpotent group
P. Hall completion

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10.1016/j.apal.2011.04.003

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title = "Groups elementarily equivalent to a free nilpotent group of finite rank",

abstract = "In this paper, we give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite rank over an arbitrary binomial domain. In particular, we characterize all groups elementarily equivalent to a free nilpotent group of finite rank.",

keywords = "Abelian deformation, Elementary equivalence, Free nilpotent group, P. Hall completion",

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year = "2011",

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doi = "10.1016/j.apal.2011.04.003",

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T1 - Groups elementarily equivalent to a free nilpotent group of finite rank

AU - Myasnikov, Alexei G.

AU - Sohrabi, Mahmood

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N2 - In this paper, we give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite rank over an arbitrary binomial domain. In particular, we characterize all groups elementarily equivalent to a free nilpotent group of finite rank.

AB - In this paper, we give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite rank over an arbitrary binomial domain. In particular, we characterize all groups elementarily equivalent to a free nilpotent group of finite rank.

KW - Abelian deformation

KW - Elementary equivalence

KW - Free nilpotent group

KW - P. Hall completion

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UR - https://www.scopus.com/pages/publications/79960132232#tab=citedBy

U2 - 10.1016/j.apal.2011.04.003

DO - 10.1016/j.apal.2011.04.003

M3 - Article

AN - SCOPUS:79960132232

SN - 0168-0072

VL - 162

SP - 916

EP - 933

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 11

ER -

Groups elementarily equivalent to a free nilpotent group of finite rank

Abstract

Keywords

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