Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups

DOI10.1515/gcc-2019-2010zbMath1435.20055arXiv1501.03097OpenAlexW2981052035WikidataQ127000882 ScholiaQ127000882MaRDI QIDQ2178749

Alexander Taam, O. G. Kharlampovich, Alexei G. Myasnikov

Publication date: 11 May 2020

Published in: Groups, Complexity, Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.03097

zbMATH Keywords

JSJ decompositionsequations over hyperbolic groupsHom-diagramsiterated generalized doublesNTQ-groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67) Algebraic geometry over groups; equations over groups (20F70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit groups for relatively hyperbolic groups. II: Makanin-Razborov diagrams.
• Elementary theory of free non-abelian groups.
• The isomorphism problem for toral relatively hyperbolic groups.
• Cyclic splittings of finitely presented groups and the canonical JSJ deccomposition
• JSJ-splittings for finitely presented groups over slender groups
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Magnus pairs in, and free conjugacy separability of, limit groups
• The structure of limit groups over hyperbolic groups
• Limit groups as limits of free groups.
• Limit groups over partially commutative groups and group actions on real cubings
• Implicit function theorem over free groups.
• Limits of relatively hyperbolic groups and Lyndon's completions.
• JSJ-decompositions of finitely presented groups and complexes of groups.
• Diophantine geometry over groups. VI: The elementary theory of a free group.
• Effective embedding of residually hyperbolic groups into direct products of extensions of centralizers
• JSJ decompositions of groups
• WORD EQUATIONS OVER GRAPH PRODUCTS
• Tarski’s problem about the elementary theory of free groups has a positive solution
• Diophantine geometry over groups VII: The elementary theory of a hyperbolic group

This page was built for publication: Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups