JournalsggdVol. 10, No. 1pp. 201–239

Quadratic equations in the Grigorchuk group

  • Igor Lysenok

    Steklov Mathematical Institute, Moscow, Russian Federation

  • Alexei Miasnikov

    Stevens Institute of Technology, Hoboken, USA

  • Alexander Ushakov

    Stevens Institute of Technology, Hoboken, USA
Quadratic equations in the Grigorchuk group cover
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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