Algorithmic Recognition of Innite-Cyclic-Extentions

Delaram Kahrobaei; Bren Cavallo; Enric Ventura; Jordi Delgado

doi:10.1016/j.jpaa.2016.10.008

Algorithmic Recognition of Innite-Cyclic-Extentions

Delaram Kahrobaei, Bren Cavallo, Enric Ventura, Jordi Delgado

Computer Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2157-2179
Number of pages	22
Journal	Journal of Pure and Applied Algebra
Early online date	25 Oct 2016
DOIs	https://doi.org/10.1016/j.jpaa.2016.10.008
Publication status	Published - 2017

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Cite this

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title = "Algorithmic Recognition of Innite-Cyclic-Extentions",

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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AB - 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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