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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| Vydáno v: | Canadian mathematical bulletin Ročník 67; číslo 4; s. 991 - 1000 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Canada
Canadian Mathematical Society
01.12.2024
Cambridge University Press |
| Témata: | |
| ISSN: | 0008-4395, 1496-4287 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0008-4395 1496-4287 |
| DOI: | 10.4153/S0008439524000390 |