Nilpotent groups of class three and braces
Cedó, Ferran ![ORCID Identifier](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Jespens, Eric (Vrije Universiteit Brussel. Department of Mathematics)
Okniński, Jan (Warsaw University (Polònia). Institute of Mathematics)
Date: |
2016 |
Abstract: |
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. |
Rights: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Subject: |
Yang-Baxter equation ;
Set-theoretic solution ;
Brace ;
Nilpotent group ;
Metabelian group |
Published in: |
Publicacions matemàtiques, Vol. 60 Núm. 1 (2016) , p. 55-79 (Survey) , ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/302233
DOI: 10.5565/PUBLMAT_60116_03
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Record created 2015-12-23, last modified 2022-09-04