Groups, Geometry, and Dynamics


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Volume 10, Issue 1, 2016, pp. 201–239
DOI: 10.4171/GGD/348

Published online: 2016-02-09

Quadratic equations in the Grigorchuk group

Igor Lysenok[1], Alexei Miasnikov[2] and Alexander Ushakov[3]

(1) Steklov Mathematical Institute, Moscow, Russian Federation
(2) Stevens Institute of Technology, Hoboken, USA
(3) Stevens Institute of Technology, Hoboken, USA

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.

Keywords: Grigorchuck group, Diophantine problem, quadratic equations

Lysenok Igor, Miasnikov Alexei, Ushakov Alexander: Quadratic equations in the Grigorchuk group. Groups Geom. Dyn. 10 (2016), 201-239. doi: 10.4171/GGD/348