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

Effective construction of covers of canonical Hom-diagrams for equations over torsion-free... AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

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

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Publisher
de Gruyter
Copyright
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2019-2010
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2019

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