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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Veröffentlicht in:Communications in algebra Jg. 52; H. 12; S. 5150 - 5164
Hauptverfasser: Galici, Mario, Nagy, Gábor P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 01.12.2024
Taylor & Francis Ltd
Schlagworte:
Loops
nets
ISSN:0092-7872, 1532-4125
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Abstract 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.
AbstractList 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.
Author Galici, Mario
Nagy, Gábor P.
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10.1017/S0305004106009625
10.1016/j.jpaa.2015.07.014
10.1090/S0002-9947-07-04391-7
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10.4153/CJM-1994-059-8
10.1515/9783110900583
10.1017/S030500419900403X
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Snippet 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...
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Title An extension formula for right Bol loops arising from Bol reflections
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