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

Olga Kharlampovich, Alexei Myasnikov, Alexander Taam

Research output: Contribution to journalArticlepeer-review

Abstract

We show that, given a finitely generated group G as the coordinate group of a finite system of equations over a torsion-free hyperbolic group Γ, there is an algorithm which constructs a cover of a canonical solution diagram. The diagram encodes all homomorphisms from G to Γ as compositions of factorizations through Γ-NTQ groups and canonical automorphisms of the corresponding NTQ-subgroups. We also give another characterization of Γ-limit groups as iterated generalized doubles over Γ.

Original languageEnglish
Pages (from-to)83-101
Number of pages19
JournalGroups, Complexity, Cryptology
Volume11
Issue number2
DOIs
StatePublished - 1 May 2019

Keywords

  • Equations over hyperbolic groups
  • Hom-diagrams
  • JSJ decompositions
  • NTQ-groups
  • iterated generalized doubles

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