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Algorithmic recognition of infinite cyclic extensions
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.Peer ReviewedPostprint (author's final draft- Article
- 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
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Last time updated on 01/05/2017
This paper was published in UPCommons. Portal del coneixement obert de la UPC.
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