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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Teerapong Suksumran | en_US |
dc.date.accessioned | 2022-10-16T07:00:26Z | - |
dc.date.available | 2022-10-16T07:00:26Z | - |
dc.date.issued | 2022-12-01 | en_US |
dc.identifier.issn | 00224049 | en_US |
dc.identifier.other | 2-s2.0-85130311153 | en_US |
dc.identifier.other | 10.1016/j.jpaa.2022.107134 | en_US |
dc.identifier.uri | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130311153&origin=inward | en_US |
dc.identifier.uri | http://cmuir.cmu.ac.th/jspui/handle/6653943832/75519 | - |
dc.description.abstract | The notion of a group action can be extended to the case of gyrogroups. In this article, we examine a digraph and graph associated with a gyrogroup action on a finite nonempty set, called a Schreier digraph and graph. We show that algebraic properties of gyrogroups and gyrogroup actions such as being gyrocommutative, being transitive, and being fixed-point-free are reflected in their Schreier digraphs and graphs. We also prove graph-theoretic versions of the three fundamental theorems involving actions: the Cauchy–Frobenius lemma (also known as the Burnside lemma), the orbit-stabilizer theorem, and the orbit decomposition theorem. Finally, we make a connection between gyrogroup actions and actions of symmetric groups by evaluation via Schreier digraphs and graphs. | en_US |
dc.subject | Mathematics | en_US |
dc.title | On Schreier graphs of gyrogroup actions | en_US |
dc.type | Journal | en_US |
article.title.sourcetitle | Journal of Pure and Applied Algebra | en_US |
article.volume | 226 | en_US |
article.stream.affiliations | Chiang Mai University | en_US |
Appears in Collections: | CMUL: Journal Articles |
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