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A class of digraph groups defined by balanced presentations

Cuno, Johannes and Williams, Gerald (2020) 'A class of digraph groups defined by balanced presentations.' Journal of Pure and Applied Algebra, 224 (8). p. 106342. ISSN 0022-4049

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We consider groups defined by non-empty balanced presentations with the property that each relator is of the form R(x,y), where x and y are distinct generators and R(.,.) is determined by some fixed cyclically reduced word R(a,b) 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.

Item Type: Article
Uncontrolled Keywords: Graph group; Balanced presentation; Deficiency zero; Rank
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 11 Feb 2020 08:33
Last Modified: 06 Jan 2022 13:51

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