The infinite Fibonacci groups and relative asphericityTools Edjvet, Martin and Juhasz, Arye (2017) The infinite Fibonacci groups and relative asphericity. Transactions of the London Mathematical Society, 4 (1). pp. 148-218. ISSN 2052-4986 Full text not available from this repository.AbstractWe 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.
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