Algorithmic recognition of infinite cyclic extensions

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Title:	Algorithmic recognition of infinite cyclic extensions
Author:	Cavallo, Bren; Delgado Rodríguez, Jordi; Kahrobaei, Delaram; Ventura Capell, Enric
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups -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
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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