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Algorithmic Recognition of Innite-Cyclic-Extentions

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JournalJournal of Pure and Applied Algebra
DateE-pub ahead of print - 25 Oct 2016
DatePublished (current) - 2017
Number of pages22
Pages (from-to)2157-2179
Early online date25/10/16
Original languageEnglish

Abstract

We prove that one cannot algorithmically decide whether a finitely presented 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 extensions, and the semi-conjugacy problem for deranged outer automorphisms.

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