Cyclically presented groups as Labelled Oriented Graph groups
Loading...
Access rights
openAccess
publishedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Authors
Date
Major/Subject
Mcode
Degree programme
Language
en
Pages
20
Series
Journal of Algebra, Volume 605, pp. 179-198
Abstract
We use results concerning the Smith forms of circulant matrices to identify when cyclically presented groups have free abelianisation and so can be Labelled Oriented Graph (LOG) groups. We generalize a theorem of Odoni and Cremona to show that for a fixed defining word, whose corresponding representer polynomial has an irreducible factor that is not cyclotomic and not equal to ±t, there are at most finitely many n for which the corresponding n-generator cyclically presented group has free abelianisation. We classify when Campbell and Robertson's generalized Fibonacci groups H(r,n,s) are LOG groups and when the Sieradski groups are LOG groups. We prove that amongst Johnson and Mawdesley's groups of Fibonacci type, the only ones that can be LOG groups are Gilbert-Howie groups H(n,m). We conjecture that if a Gilbert-Howie group is a LOG group, then it is a Sieradski group, and prove this in certain cases (in particular, for fixed m, the conjecture can only be false for finitely many n). We obtain necessary conditions for a cyclically presented group to be a connected LOG group in terms of the representer polynomial and apply them to the Prishchepov groups.Description
Funding Information: Vanni Noferini acknowledges support by an Academy of Finland grant (Suomen Akatemian päätös 331240) and partial support by the Visiting Fellows Programme of the University of Pisa.Gerald Williams was supported for part of this project by Leverhulme Trust Research Project Grant RPG-2017-334. Publisher Copyright: © 2022
Other note
Citation
Noferini, V & Williams, G 2022, 'Cyclically presented groups as Labelled Oriented Graph groups', Journal of Algebra, vol. 605, pp. 179-198. https://doi.org/10.1016/j.jalgebra.2022.04.018