Williams, G (2009) The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups. Journal of Group Theory, 12 (1). pp. 139-149. DOI https://doi.org/10.1515/JGT.2008.066
Williams, G (2009) The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups. Journal of Group Theory, 12 (1). pp. 139-149. DOI https://doi.org/10.1515/JGT.2008.066
Williams, G (2009) The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups. Journal of Group Theory, 12 (1). pp. 139-149. DOI https://doi.org/10.1515/JGT.2008.066
Abstract
The Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups are defined by the presentations Gn (m, k) = 〈x 1, … , xn | xixi+m = xi+k (1 ⩽ i ⩽ n)〉. These cyclically presented groups generalize Conway's Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn (m, k). We determine when Gn (m, k) has infinite abelianization and provide sufficient conditions for Gn (m, k) to be perfect. We conjecture that these are also necessary conditions. Combined with our asphericity theorem, a proof of this conjecture would imply a classification of the finite Cavicchioli–Hegenbarth–Repovš groups.
Item Type: | Article |
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Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 04 Jan 2012 12:02 |
Last Modified: | 16 May 2024 18:30 |
URI: | http://repository.essex.ac.uk/id/eprint/1811 |
Available files
Filename: $002fj$002fjgth.2009.12.issue-1$002fjgt.2008.066$002fjgt.2008.066.pdf