| Título: | Membership problem in groups acting freely on non-archimedean trees |
| Autores: | Nikolaev, Andrey |
| Fecha: | 2010 |
| Publicador: | McGill University |
| Fuente: |
Ver documento |
| Tipo: | Electronic Thesis or Dissertation |
| Tema: | Pure Sciences - Mathematics |
| Descripción: |
Groups acting freely on $\mathbb Z^n$-trees ($\mathbb Z^n$-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of $\mathbb Z^n$-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in $\mathbb Z^n$-free groups. Les groupes agissant librement sur les $\mathbb Z^n$-arbres (les groupes $\mathbb Z^n$-libres) ont un rôle clé dans l'étude des actions non-archimédiennes de groupes. Suite aux idées de Stallings, nous développons des techniques graphes-théoretique afin d'étudier la structure de sous-groupes des groupes $\mathbb Z^n$-libres. Une des applications immédiate de notre méthode, est une solution algorithmique du Problème d'Occurance Uniforme et du Problème de Puissance dans les groupes $\mathbb Z^n$-libres. |
| Idioma: | en |
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