The infinite Fibonacci groups and relative asphericity

Edjvet, Martin; Juhasz, Arye

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.

Citation

Edjvet, M., & Juhasz, A. (2017). The infinite Fibonacci groups and relative asphericity. Transactions of the London Mathematical Society, 4(1), https://doi.org/10.1112/tlm3.12007

• Journal Article Type: Article
• Acceptance Date: Aug 9, 2017
• Online Publication Date: Oct 2, 2017
• Publication Date: Dec 31, 2017
• Deposit Date: Mar 23, 2017
• Publicly Available Date: Oct 2, 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
• Public URL: https://nottingham-repository.worktribe.com/output/902510
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1112/tlm3.12007/abstract
• Contract Date: Mar 23, 2017