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The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups

Williams, G (2009) 'The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups.' Journal of Group Theory, 12 (1). 139 - 149. ISSN 1433-5883

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 12:02
Last Modified: 09 Mar 2018 10:15
URI: http://repository.essex.ac.uk/id/eprint/1811

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