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The infinite Fibonacci groups and relative asphericity

Edjvet, Martin; Juhasz, Arye

Authors

Martin Edjvet martin.edjvet@nottingham.ac.uk

Arye Juhasz arju@techunix.technion.ac.il

Abstract

We prove that the generalised Fibonacci group F (r, n) is infinite for (r, n) ∈ {(7 + 5k, 5), (8 + 5k, 5) : k ≥ 0}. This together with previously known results yields a complete classification of the finite F (r, n), a problem that has its origins in a question by J H Conway in 1965. The method is to show that a related relative presentation is aspherical from which it can be deduced that the groups are infinite.

Journal Article Type Article
Publication Date Dec 31, 2017
Journal Transactions of the London Mathematical Society
Electronic ISSN 2052-4986
Publisher London Mathematical Society
Peer Reviewed Peer Reviewed
Volume 4
Issue 1
DOI https://doi.org/10.1112/tlm3.12007
Publisher URL http://onlinelibrary.wiley.com/doi/10.1112/tlm3.12007/abstract
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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