The infinite Fibonacci groups and relative asphericityTools Edjvet, Martin and Juhasz, A. (2017) The infinite Fibonacci groups and relative asphericity. Technical Report. London Mathematical Society. (Unpublished)
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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