Nilpotent groups of class three and braces

Ferran Cedó, Eric Jespers, J. Okninski

Research output: Contribution to journalArticle

10 Citations (Scopus)


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 $[H,H]
\subseteq \Soc (H)$ and $H/[H,H]$ is a standard abelian brace,
where $\Soc (H)$ denotes the socle of the brace $H$.
Original languageEnglish
Pages (from-to)55-79
Number of pages16
JournalPublicacions Matemàtiques
Issue number1
Publication statusPublished - 2016


  • Yang-Baxter equation
  • set-theoretic solution
  • brace
  • nilpotent group
  • metabelian group

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