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A class of digraph groups defined by balanced presentations.

  • We consider groups defined by non-empty balanced presentations with the property that each relator is of the form, where x and y are distinct generators and is determined by some fixed cyclically reduced word that involves both a and b. To every such presentation we associate a directed graph whose vertices correspond to the generators and whose arcs correspond to the relators. Under the hypothesis that the girth of the underlying undirected graph is at least 4, we show that the resulting groups are non-trivial and cannot be finite of rank 3 or higher. Without the hypothesis on the girth it is well known that both the trivial group and finite groups of rank 3 can arise.

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Author:Johannes Cuno, Gerald Williams
Document Type:Working Paper
Publishing Institution:P├Ądagogische Hochschule Ludwigsburg
Release Date:2023/01/26
Year of Completion:2020
Tag:digraph groups
GND Keyword:Mathematik
Issue:Journal of Pure and Applied Algebra (224) 8, 2020
Volltext ist unter angegebener DOI abrufbar.
DDC class:500 Naturwissenschaften und Mathematik / 510 Mathematik
Open Access:Ja
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International