Generalizations of word and conjugacy problems in right angled artin groups
In 2008 Crisp, Godelle and Wiest introduced the idea of piling to give a linear time solution to the word and conjugacy problem in Right Angled Artin groups. In this master’s thesis we push forward that idea by generalizing it to efficiently solve the word and conjugacy problem in Partially Commutat...
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| Formato: | tesis de maestría |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/415238 |
| Acesso em linha: | https://hdl.handle.net/2117/415238 |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph theory RAAG Artin Group Partially commutative group Word problem Conjugacy problem Graph group Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | In 2008 Crisp, Godelle and Wiest introduced the idea of piling to give a linear time solution to the word and conjugacy problem in Right Angled Artin groups. In this master’s thesis we push forward that idea by generalizing it to efficiently solve the word and conjugacy problem in Partially Commutative products of groups. Also, the idea of pilings can be used to understand the structure of Right Angled Artin groups because it is a form of computing normal form of elements. This is also used to solve a collective version of the word problem. At the end of the thesis I also propose a generalization of RAAGs based on hypergraphs which contains as an example the Heisenberg group. This last generalization would be interesting to study if we manage to prove an isomorphism theorem between hypergraphs and hypergraph groups. |
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