Quadratic equations in the grigorchuk group

Igor Lysenok; Alexei Miasnikov; Alexander Ushakov

doi:10.4171/GGD/348

Quadratic equations in the grigorchuk group

Department of Mathematical Sciences

RAS - Steklov Mathematical Institute
Stevens Institute of Technology

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

14 Scopus citations

Abstract

We prove that the Diophantine problem for quadratic equations in the Grigorchuk group is algorithmically solvable. As a corollary to our approach, we prove that the group has a finite commutator width.

Original language	English
Pages (from-to)	201-239
Number of pages	39
Journal	Groups, Geometry, and Dynamics
Volume	10
Issue number	1
DOIs	https://doi.org/10.4171/GGD/348
State	Published - 2016

Keywords

Diophantine problem
Grigorchuck group
Quadratic equations

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10.4171/GGD/348

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title = "Quadratic equations in the grigorchuk group",

abstract = "We prove that the Diophantine problem for quadratic equations in the Grigorchuk group is algorithmically solvable. As a corollary to our approach, we prove that the group has a finite commutator width.",

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AU - Lysenok, Igor

AU - Miasnikov, Alexei

AU - Ushakov, Alexander

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N2 - We prove that the Diophantine problem for quadratic equations in the Grigorchuk group is algorithmically solvable. As a corollary to our approach, we prove that the group has a finite commutator width.

AB - We prove that the Diophantine problem for quadratic equations in the Grigorchuk group is algorithmically solvable. As a corollary to our approach, we prove that the group has a finite commutator width.

KW - Diophantine problem

KW - Grigorchuck group

KW - Quadratic equations

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U2 - 10.4171/GGD/348

DO - 10.4171/GGD/348

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SP - 201

EP - 239

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 1

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Quadratic equations in the grigorchuk group

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Keywords

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