The conjugacy problem in extensions of Thompson’s group F

We solve the twisted conjugacy problem on Thompson’s group F . We also exhibit orbit undecidable subgroups of Aut( F ), and give a proof that Aut( F ) and Aut + ( F ) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski,...

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Bibliographic Details
Published in:Israel journal of mathematics Vol. 216; no. 1; pp. 15 - 59
Main Authors: Burillo, José, Matucci, Francesco, Ventura, Enric
Format: Journal Article Publication
Language:English
Published: Jerusalem The Hebrew University Magnes Press 01.10.2016
Springer Nature B.V
Subjects:
14 Algebraic geometry
14Q Computational aspects in algebraic geometry
65 Numerical analysis
65D Numerical approximation and computational geometry
Algebra
Analysis
Applications of Mathematics
Classificació AMS
Geometria
Geometria algebraica
Geometria algèbrica
Geometria computacional
Geometry, Algebraic
Group Theory and Generalizations
Matemàtiques i estadística
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Subgroups
Theoretical
Àrees temàtiques de la UPC
ISSN:0021-2172, 1565-8511
Online Access:Get full text
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Summary:We solve the twisted conjugacy problem on Thompson’s group F . We also exhibit orbit undecidable subgroups of Aut( F ), and give a proof that Aut( F ) and Aut + ( F ) are orbit decidable provided a certain conjecture on Thompson’s group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak–Fel’shtyn–Gonçalves in [4] showing that F has property R ∞ , and which can be extended to show that Thompson’s group T also has property R ∞ .
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content type line 14
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1403-9