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Groups of Fibonacci type revisited

Williams, G (2012) 'Groups of Fibonacci type revisited.' International Journal of Algebra and Computation, 22 (8). p. 1240002. ISSN 0218-1967


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This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups.

Item Type: Article
Uncontrolled Keywords: Fibonacci group; Fibonacci semigroup; Cyclically presented group; Labelled Oriented Graph (LOG) group; small cancellation theory; asphericity
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 06 Sep 2012 11:02
Last Modified: 18 Aug 2022 11:35

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