Finite automata for Schreier graphs of virtually free groups
The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows efficient computation of the core of a Schreier graph based on edge folding. It is proved that the groups that admit Stallings sections are precisely the f.g. vir...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2016 |
| 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:2117/83851 |
| Acesso em linha: | https://hdl.handle.net/2117/83851 https://dx.doi.org/10.1515/jgth-2015-0028 |
| Access Level: | acceso abierto |
| Palavra-chave: | Group theory Virtually free groups Stallings foldings Schreier graphs Nitely generated subgroups Grups, Teoria de Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Resumo: | The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows efficient computation of the core of a Schreier graph based on edge folding. It is proved that the groups that admit Stallings sections are precisely the f.g. virtually free groups, this is proved through a constructive approach based on Bass-Serre theory. Complexity issues and applications are also discussed. |
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