An extension formula for right Bol loops arising from Bol reflections

We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint uni...

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Vydané v:Communications in algebra Ročník 52; číslo 12; s. 5150 - 5164
Hlavní autori: Galici, Mario, Nagy, Gábor P.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 01.12.2024
Taylor & Francis Ltd
Predmet:
Loops
nets
ISSN:0092-7872, 1532-4125
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Shrnutí:We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint union of two isomorphic involutory quandles. We also derive further results on the structure group of the core of the extension.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2367161