Quadratic equations in the Grigorchuk group.

DOI10.4171/GGD/348zbMath1341.20037arXiv1304.5579OpenAlexW2962823911MaRDI QIDQ260112

Alexander Ushakov, Igor G. Lysenok, Alexei G. Myasnikov

Publication date: 18 March 2016

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5579

zbMATH Keywords

equations over groupsDiophantine problemGrigorchuck groupproducts of commutatorsquadratic equations

Mathematics Subject Classification ID

Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Commutator calculus (20F12) Groups acting on trees (20E08) Algebraic geometry over groups; equations over groups (20F70)

Related Items (8)

Verbal subgroups of hyperbolic groups have infinite width ⋮ Quadratic equations in metabelian Baumslag–Solitar groups ⋮ On commutator subgroups of Sylow 2-subgroups of the alternating group, and the commutator width in wreath products ⋮ Orientable quadratic equations in free metabelian groups ⋮ Explicit solutions of certain orientable quadratic equations in free groups ⋮ Diophantine problems in solvable groups ⋮ Linear time algorithm for the conjugacy problem in the first Grigorchuk group ⋮ Commutator width in the first Grigorchuk group

Cites Work

• The conjugacy problem in the Grigorchuk group is polynomial time decidable.
• Quadratic equations over free groups and free products
• Elementary theory of free non-abelian groups.
• On Burnside's problem on periodic groups
• Conjugacy problem in an automorphism group of an infinite tree
• Irreducible affine varieties over a free group. II: Systems in triangular quasi-quadratic form and description of residually free groups
• On systems of equations over free partially commutative groups
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