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

Olga Kharlampovich EMAIL logo , Alexei Myasnikov and Alexander Taam

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.

MSC 2010: 20F70; 20F67

Acknowledgements

We would like to thank N. Touikan for the important comments which helped improving the quality of the paper.

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Received: 2018-10-17
Published Online: 2019-10-16
Published in Print: 2019-11-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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