Open Access
2016 Nilpotent Groups of Class Three and Braces
Ferran Cedó, Eric Jespers, Jan OkniŃski
Publ. Mat. 60(1): 55-79 (2016).


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 $[H,H] \subseteq \operatorname{Soc} (H)$ and $H/[H,H]$ is a standard abelian brace, where $\operatorname{Soc} (H)$ denotes the socle of the brace $H$.


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Ferran Cedó. Eric Jespers. Jan OkniŃski. "Nilpotent Groups of Class Three and Braces." Publ. Mat. 60 (1) 55 - 79, 2016.


Published: 2016
First available in Project Euclid: 22 December 2015

zbMATH: 1345.16039
MathSciNet: MR3447734

Primary: 16T25 , 20F16 , 20F18

Keywords: brace , Metabelian group , nilpotent group , ‎set-theoretic solution‎ , Yang--Baxter equation

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 1 • 2016
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