Strong digraph groups

A digraph group is a group defined by non-empty presentation with the property that each relator is of the form $R(x, y)$ , where x and y are distinct generators and $R(\cdot , \cdot )$ is determined by some fixed cyclically reduced word $R(a, b)$ that involves both a and b. Associated with each suc...

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Veröffentlicht in:Canadian mathematical bulletin Jg. 67; H. 4; S. 991 - 1000
Hauptverfasser: Cihan, Mehmet Sefa, Williams, Gerald
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Canada Canadian Mathematical Society 01.12.2024
Cambridge University Press
Schlagworte:
Apexes
Graph theory
Digraph group
digraph products
05C20
Cayley digraph
05C40
20F05
05C25
05C38
strong digraph
circulant digraph
ISSN:0008-4395, 1496-4287
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Zusammenfassung:A digraph group is a group defined by non-empty presentation with the property that each relator is of the form $R(x, y)$ , where x and y are distinct generators and $R(\cdot , \cdot )$ is determined by some fixed cyclically reduced word $R(a, b)$ that involves both a and b. Associated with each such presentation is a digraph whose vertices correspond to the generators and whose arcs correspond to the relators. In this article, we consider digraph groups for strong digraphs that are digon-free and triangle-free. We classify when the digraph group is finite and show that in these cases it is cyclic, giving its order. We apply this result to the Cayley digraph of the generalized quaternion group, to circulant digraphs, and to Cartesian and direct products of strong digraphs.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439524000390