Stallings automata and applications : BGSMath graduate course
The goal of this Advanced Graduate Course is to introduce the student into the world of free groups, to show the intrinsic complexity of this algebraic structure and of the natural problems emanating from it, and to introduce the modern Stallings techniques, able to solve most of the classical probl...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2023 |
| 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:2117/395113 |
| Acceso en línea: | https://hdl.handle.net/2117/395113 https://dx.doi.org/10.13140/RG.2.2.31871.69281/1 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Grups, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | The goal of this Advanced Graduate Course is to introduce the student into the world of free groups, to show the intrinsic complexity of this algebraic structure and of the natural problems emanating from it, and to introduce the modern Stallings techniques, able to solve most of the classical problems and many new ones in a quite comprehensible and graphical way. We’ll emphasize the computational point of view, not just giving formal proofs, but also providing algorithms able to do the tasks effectively. The course will cover several classical results, like Nielsen-Schreier Theorem, Schreier index formula, Marshall Hall Theorem, membership problem, residual finiteness, the Howson property, Hanna-Neumann inequality, etc. But we plan to also introduce more advanced material in direct connection with research done in the last years: techniques for giving asymptotic estimates of properties of subgroups of the free group, enriched Stallings graphs allowing to extend results to broader families. |
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