The infinite Fibonacci groups and relative asphericity
We 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 t...
| Main Authors: | , |
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| Format: | Article |
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London Mathematical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41401/ |
| _version_ | 1848796265846931456 |
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| author | Edjvet, Martin Juhasz, Arye |
| author_facet | Edjvet, Martin Juhasz, Arye |
| author_sort | Edjvet, Martin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We 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. |
| first_indexed | 2025-11-14T19:45:14Z |
| format | Article |
| id | nottingham-41401 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:45:14Z |
| publishDate | 2017 |
| publisher | London Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-414012020-05-04T19:24:56Z https://eprints.nottingham.ac.uk/41401/ The infinite Fibonacci groups and relative asphericity Edjvet, Martin Juhasz, Arye We 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. London Mathematical Society 2017-12-31 Article PeerReviewed 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 http://onlinelibrary.wiley.com/doi/10.1112/tlm3.12007/abstract doi:10.1112/tlm3.12007 doi:10.1112/tlm3.12007 |
| spellingShingle | Edjvet, Martin Juhasz, Arye The infinite Fibonacci groups and relative asphericity |
| title | The infinite Fibonacci groups and relative asphericity |
| title_full | The infinite Fibonacci groups and relative asphericity |
| title_fullStr | The infinite Fibonacci groups and relative asphericity |
| title_full_unstemmed | The infinite Fibonacci groups and relative asphericity |
| title_short | The infinite Fibonacci groups and relative asphericity |
| title_sort | infinite fibonacci groups and relative asphericity |
| url | https://eprints.nottingham.ac.uk/41401/ https://eprints.nottingham.ac.uk/41401/ https://eprints.nottingham.ac.uk/41401/ |