The conjugacy problem for free-by-cyclic groups
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed sub- groups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic w...
| Autores: | , |
|---|---|
| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2004 |
| 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:2117/79985 |
| Acceso en línea: | https://hdl.handle.net/2117/79985 |
| Access Level: | acceso abierto |
| Palabra clave: | Free groups Group theory Grups, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Sumario: | We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed sub- groups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power of a given automorphism. The algorithm effectively computes a conjugating element, if it exists. We also solve the power conjugacy problem and give an algorithm to rec- ognize if two given elements of a finitely generated free group are Reidemeister equivalent with respect to a given automorphism. |
|---|