Implicit function theorem over free groups.

DOI10.1016/j.jalgebra.2005.04.001zbMath1094.20016arXivmath/0312509OpenAlexW1994502794MaRDI QIDQ2386057

O. G. Kharlampovich, Alexei G. Myasnikov

Publication date: 22 August 2005

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

Full work available at URL: https://arxiv.org/abs/math/0312509

zbMATH Keywords

decidabilityfree groupsimplicit function theoremsalgebraic geometrySkolem functionsequations in free groupsTarski problemsregular NTQ systemsregular quadratic equations

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Model-theoretic algebra (03C60) Decidability of theories and sets of sentences (03B25) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items

LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS, Groups with free regular length functions in $\mathbb{Z}^{n}$, Random equations in free groups, Algorithmic undecidability of compatibility problem for equations in free groups: explicit equations with one commutator-type constraint, Magnus pairs in, and free conjugacy separability of, limit groups, ON POSITIVE THEORIES OF GROUPS WITH REGULAR FREE LENGTH FUNCTIONS, Andrews–Curtis groups and the Andrews–Curtis conjecture, Elementary theory of free non-abelian groups., The isomorphism problem for finitely generated fully residually free groups., Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups, On pro-\(p\) analogues of limit groups via extensions of centralizers., Pregroups and the big powers condition., On Turner’s theorem and first-order theory, A product theorem in free groups., On systems of equations over free products of groups., LIMIT GROUPS ARE CONJUGACY SEPARABLE, Subgroup properties of pro-\(p\) extensions of centralizers., ALGEBRAIC LOGIC AND LOGICALLY-GEOMETRIC TYPES IN VARIETIES OF ALGEBRAS, Subgroup properties of fully residually free groups, DEFINABLE SETS IN A HYPERBOLIC GROUP, A note on Lyndon properties in one-relator groups., The RSA group is pseudo-free, A polynomial bound on solutions of quadratic equations in free groups., Solving one-variable equations in free groups, On systems of equations over free partially commutative groups, Fields definable in the free group, Quadratic properties in group amalgams, Limit groups over partially commutative groups and group actions on real cubings, Quadratic equations in hyperbolic groups are NP-complete

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New estimates of odd exponents of infinite Burnside groups.
• Pregroups and the big powers condition.
• Quadratic equations over free groups and free products
• The equation \(a^2b^2=c^2\) in free groups
• Lower bounds on the size of bounded depth circuits over a complete basis with logical addition
• The verbal topology of a group
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
• Irreducible affine varieties over a free group. II: Systems in triangular quasi-quadratic form and description of residually free groups
• Model theory
• Linear groups with bounded cyclic subgroups
• \(\exists\)-free groups
• DECIDABILITY OF THE UNIVERSAL AND POSITIVE THEORIES OF A FREE GROUP
• Tarski’s problem about the elementary theory of free groups has a positive solution
• ON RESIDUALING HOMOMORPHISMS AND G-SUBGROUPS OF HYPERBOLIC GROUPS
• EXPONENTIAL GROUPS 2: EXTENSIONS OF CENTRALIZERS AND TENSOR COMPLETION OF CSA-GROUPS
• CSA-groups and separated free constructions