Geodesic
Quadratic equations in the Grigorchuk group
Igor Lysenok1 ; Alexei Miasnikov2 ; Alexander Ushakov2
1Steklov Mathematical Institute, Moscow, Russian Federation
2Stevens Institute of Technology, Hoboken, USA
Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 201-239

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DOI

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.
DOI : 10.4171/ggd/348
Classification : 68-XX, 11-XX, 20-XX
Mots-clés : Grigorchuck group, Diophantine problem, quadratic equations

Igor Lysenok  1   ; Alexei Miasnikov  2   ; Alexander Ushakov  2

1 Steklov Mathematical Institute, Moscow, Russian Federation
2 Stevens Institute of Technology, Hoboken, USA 
Igor Lysenok; Alexei Miasnikov; Alexander Ushakov. Quadratic equations in the Grigorchuk group. Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 201-239. doi: 10.4171/ggd/348
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     title = {Quadratic equations in the {Grigorchuk} group},
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     pages = {201--239},
     year = {2016},
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     number = {1},
     doi = {10.4171/ggd/348},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/348/}
}
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