Nilpotent groups of class three and braces
New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang-Baxter equation. In particular, it follows that if a group G of odd order is nilpotent of class three, then it is a homomorphic image of the multiplicative group of a finite left brace...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:144962 |
| Acceso en línea: | https://ddd.uab.cat/record/144962 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_60116_03 |
| Access Level: | acceso abierto |
| Palabra clave: | Yang-Baxter equation Set-theoretic solution Brace Nilpotent group Metabelian group |
| Sumario: | New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang-Baxter equation. In particular, it follows that if a group G of odd order is nilpotent of class three, then it is a homomorphic image of the multiplicative group of a finite left brace (i.e. an involutive Yang-Baxter group) which also is a nilpotent group of class three. We give necessary and sufficient conditions for an arbitrary group H to be the multiplicative group of a left brace such that [H, H] ⊆ Soc(H) and H/[H, H] is a standard abelian brace, where Soc(H) denotes the socle of the brace H. |
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