English

Algorithmic recognition of infinite cyclic extensions

Group Theory 2016-10-04 v2

Abstract

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

Keywords

Cite

@article{arxiv.1509.05879,
  title  = {Algorithmic recognition of infinite cyclic extensions},
  author = {Bren Cavallo and Jordi Delgado and Delaram Kahrobaei and Enric Ventura},
  journal= {arXiv preprint arXiv:1509.05879},
  year   = {2016}
}

Comments

24 pages

R2 v1 2026-06-22T11:00:32.510Z