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arXiv · 1708.01194

The infinite Fibonacci groups and relative asphericity

M. Edjvet·A. Juhasz
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Abstract

We prove that the generalised Fibonacci group F(r,n) is infinite for (r,n) in {(7 + 5k,5), (8 + 5k,5)} where k is greater than or equal to 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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M. Edjvet, A. Juhasz. 2017-08-03. The infinite Fibonacci groups and relative asphericity. https://doi.org/10.1112/tlm3.12007

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