Nilpotent groups of class three and braces

Ferran Cedó, Eric Jespers, Jan Okniński

Research output: Contribution to journalArticleResearchpeer-review

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] ⊂ 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
JournalPublicacions Matematiques
Publication statusPublished - 1 Jan 2016


  • Brace
  • Metabelian group
  • Nilpotent group
  • Set-theoretic solution
  • Yang-Baxter equation


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