The Gap between an automorphism and its Inverse
We reintroduce the function alpha_G (and beta_G) that measures the gap between an (outer) automorphism of $G$ and its inverse. We give an alternative proof of the lower bound for alpha_{F_r} of the free groups, and give an improvement for the lower bound of beta_{F_r}. Furthermore, for the first tim...
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| Tipo de recurso: | tesis de maestría |
| 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:2117/349209 |
| Acceso en línea: | https://hdl.handle.net/2117/349209 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Group Automorphism Inverse automorphism Auto-gap function Norm of an automorphism Outer automorphism Outer-gap function Free group Baumslag-Solitar group Virtual automorphisms Schreier graph Virtual-gap function Grups finits Grups infinits 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: | We reintroduce the function alpha_G (and beta_G) that measures the gap between an (outer) automorphism of $G$ and its inverse. We give an alternative proof of the lower bound for alpha_{F_r} of the free groups, and give an improvement for the lower bound of beta_{F_r}. Furthermore, for the first time, a study of the function alpha_{BS(1,N)} for the Baumslag-Solitar groups BS(1,N), |N|>1, is made, and we prove that it grows linearly. Finally, in an independent way, we define the same concept over the virtual automorphisms and prove that the equivalent function for the free groups has an exponential lower bound. |
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