Groupoids: Direct products, semidirect products and solvability

We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direc...

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Datum:2022
Hauptverfasser: Marín, V., Pinedo, H.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2022
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Zusammenfassung:We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid \(\mathcal{G}\) is solvable if and only if its isotropy groups are.