Per citar aquest document: http://ddd.uab.cat/record/144962
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)

Data: 2016
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Yang-Baxter equation ; Set-theoretic solution ; Brace ; Nilpotent group ; Metabelian group
Publicat a: Publicacions matemàtiques, Vol. 60 Núm. 1 (2016) , p. 55-79 (Survey) , ISSN 2014-4350

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT%2060116%2003
DOI: 10.5565/10.5565-PUBLMAT 60116 03


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