Groups elementarily equivalent to the classical matrix groups

Alexei G. Myasnikov; Mahmood Sohrabi

doi:10.1515/9783111473574-004

Groups elementarily equivalent to the classical matrix groups

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as GL_n(F), SL_n(F), and T_n(F) over a field F provided n ≥3.

Original language	English
Title of host publication	Finitely Presented Groups
Subtitle of host publication	With Applications in Post-Quantum Cryptography and Artificial Intelligence
Pages	53-86
Number of pages	34
ISBN (Electronic)	9783111473574
DOIs	https://doi.org/10.1515/9783111473574-004
State	Published - 7 Oct 2024

Keywords

Abelian deformation
Biinterpretability
Elementary equivalence
First-order equivalence
General linear group
Special linear group

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10.1515/9783111473574-004

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abstract = "In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as GLn(F), SLn(F), and Tn(F) over a field F provided n ≥3.",

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AU - Sohrabi, Mahmood

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N2 - In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as GLn(F), SLn(F), and Tn(F) over a field F provided n ≥3.

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KW - Abelian deformation

KW - Biinterpretability

KW - Elementary equivalence

KW - First-order equivalence

KW - General linear group

KW - Special linear group

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EP - 86

BT - Finitely Presented Groups

ER -

Groups elementarily equivalent to the classical matrix groups

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Keywords

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