Computation of endo-fixed closures in free-abelian times free groups
In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup H of a FATF group G , decides whether H is the fixed subgroup of some (finite) family of endomorphisms of G and...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| 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:2117/446199 |
| Acceso en línea: | https://hdl.handle.net/2117/446199 https://dx.doi.org/10.1515/forum-2023-0471 |
| Access Level: | acceso abierto |
| Palabra clave: | Free-abelian times free Endomorphism Fixed subgroup Endo-fixed closure Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups Classificació AMS::20 Group theory and generalizations::20K Abelian groups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup H of a FATF group G , decides whether H is the fixed subgroup of some (finite) family of endomorphisms of G and, in the affirmative case, finds such a family. The algorithm combines both combinatorial and algebraic methods. |
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