Algorithmic recognition of infinite cyclic extensions
We prove that one cannot algorithmically decide whether a finitely presented Z-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the equivalence between the isomorphism problem within the subclass of unique Z...
| 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:2117/96690 |
| Acesso em linha: | https://hdl.handle.net/2117/96690 https://dx.doi.org/10.1016/j.jpaa.2016.10.008 |
| Access Level: | acceso abierto |
| Palavra-chave: | Group theory Finite groups Automorphisms extension cyclic extension decision problem BNS invariant undecidability Grups, Teoria de Grups finits Automorfismes 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::Àlgebra::Teoria de grups |
| Resumo: | We prove that one cannot algorithmically decide whether a finitely presented Z-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the equivalence between the isomorphism problem within the subclass of unique Z-extensions, and the semi-conjugacy problem for deranged outer automorphisms. |
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