An irrational-slope Thompson’s group
The purpose of this paper is to study the properties of the irrational-slope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, i...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/365461 |
| Acceso en línea: | https://hdl.handle.net/2117/365461 https://dx.doi.org/10.5565/PUBLMAT6522112 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Thompson’s group Irrational-slope Normal forms Distortion Grups infinits Grups finits Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | The purpose of this paper is to study the properties of the irrational-slope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson’s group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of F in Ft are undistorted. |
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