Nilpotent groups of class three and braces
Cedó, Ferran (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.
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

25 p, 363.8 KB

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