English

The infinite Fibonacci groups and relative asphericity

Group Theory 2017-10-11 v1

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.

Keywords

Cite

@article{arxiv.1708.01194,
  title  = {The infinite Fibonacci groups and relative asphericity},
  author = {M. Edjvet and A. Juhasz},
  journal= {arXiv preprint arXiv:1708.01194},
  year   = {2017}
}

Comments

106 pages, 64 figures

R2 v1 2026-06-22T21:05:53.462Z