Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups
The classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite order automorph...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:2117/184934 |
| Acceso en línea: | https://hdl.handle.net/2117/184934 https://dx.doi.org/10.1016/j.jpaa.2019.106210 |
| Access Level: | acceso abierto |
| Palabra clave: | Free-abelian times free Automorphism Fixed subgroup Periodic subgroup Auto-fixed closure Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | The classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite order automorphisms is uniformly bounded in terms of m, n. We also studyperiodic points of endomorphisms of Zm×Fn, and give an algorithm to compute auto-fixed closures of finitely generated subgroups of Zm×Fn. On the way, we prove the analog of Day’sTheorem for real elements in Zm×Fn, contributing a modest step into the project of doing sofor any right angled Artin group (as McCool did with respect to Whitehead’s Theorem in the free context). |
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