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The infinite Fibonacci groups and relative asphericity

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 Added by Martin Edjvet Dr
 Publication date 2017
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and research's language is English




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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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