TY - JOUR
T1 - Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
AU - Taam, Alexander
N1 - Publisher Copyright:
© 2019, Episciences. All rights reserved.
PY - 2019/5/1
Y1 - 2019/5/1
N2 - 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.
AB - 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.
KW - Equations over hyperbolic groups
KW - Hom-diagrams
KW - JSJ decompositions
KW - NTQ-groups
KW - iterated generalized doubles
UR - http://www.scopus.com/inward/record.url?scp=85074249326&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074249326&partnerID=8YFLogxK
U2 - 10.1515/gcc-2019-2010
DO - 10.1515/gcc-2019-2010
M3 - Article
AN - SCOPUS:85074249326
SN - 1867-1144
VL - 11
SP - 83
EP - 101
JO - Groups, Complexity, Cryptology
JF - Groups, Complexity, Cryptology
IS - 2
ER -