Quadratic equations over free groups and free products

DOI10.1016/0021-8693(81)90265-9zbMath0526.20024OpenAlexW2025953515MaRDI QIDQ595015

Charles C. Edmunds, Leo P. jun. Comerford

Publication date: 1981

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(81)90265-9

zbMATH Keywords

algorithmfree productsfree groupsalgorithmically solvable equationscommutator problemsquadratic equations over free group

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (26)

LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS ⋮ Algorithmic undecidability of compatibility problem for equations in free groups: explicit equations with one commutator-type constraint ⋮ Hyperbolic Surfaces and Quadratic Equations in Groups ⋮ Implicit function theorem over free groups. ⋮ The genus problem for one-relator products of locally indicable groups ⋮ Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz ⋮ Quadratic equations over small cancellation groups ⋮ On systems of equations over free products of groups. ⋮ The solvability problem for quadratic equations over free groups is NP-complete ⋮ The nonorientable genus problem for one-relator products ⋮ The two variable substitution problem for free products of groups ⋮ Orientable quadratic equations in free metabelian groups ⋮ A polynomial bound on solutions of quadratic equations in free groups. ⋮ On the rank of quadratic equations in free groups ⋮ Solutions of quadratic equations in groups with small cancellation condition ⋮ Homomorphism diagrams of surface groups ⋮ On systems of equations over free partially commutative groups ⋮ Gleichungen in freien Produkten mit Amalgam ⋮ Algebraic geometry over groups. I: Algebraic sets and ideal theory ⋮ Limit groups over partially commutative groups and group actions on real cubings ⋮ Commutator width in the first Grigorchuk group ⋮ Model-theoretic and algorithmic questions in group theory ⋮ Tarski’s problem about the elementary theory of free groups has a positive solution ⋮ Quadratic equations in hyperbolic groups are NP-complete ⋮ Asymptotic invariants, complexity of groups and related problems ⋮ Quadratic equations in the Grigorchuk group.

Cites Work

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• Commutators in Free Products
• Equations in Free Groups
• Commutators in Free Groups
• On the endomorphism problem for free groups
• On the Endomorphism Problem for Free Groups II
• On the Substitution Problem for Free Groups

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