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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 afinite 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

Nilpotent groups of class three and braces