Quadratic equations in the Grigorchuk group
Igor Lysenok
Steklov Mathematical Institute, Moscow, Russian FederationAlexei Miasnikov
Stevens Institute of Technology, Hoboken, USAAlexander Ushakov
Stevens Institute of Technology, Hoboken, USA
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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.
Cite this article
Igor Lysenok, Alexei Miasnikov, Alexander Ushakov, Quadratic equations in the Grigorchuk group. Groups Geom. Dyn. 10 (2016), no. 1, pp. 201–239
DOI 10.4171/GGD/348