An extension formula for right Bol loops arising from Bol reflections
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909347574972416 |
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| author | Galici, Mario Nagy, Gabor P. |
| author_facet | Galici, Mario Nagy, Gabor P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An extension formula for right Bol loops arising from Bol reflections Galici, Mario Nagy, Gabor P. Group Theory Combinatorics 20N05, 51E14 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. |
| title | An extension formula for right Bol loops arising from Bol reflections |
| topic | Group Theory Combinatorics 20N05, 51E14 |
| url | https://arxiv.org/abs/2410.09977 |