Abelian maps, brace blocks, and solutions to the Yang-Baxter equation

Abstract

Let G be a finite nonabelian group. We show how an endomorphism of G with abelian image gives rise to a family of binary operations { ∘ n : n ∈ Z ≥ 0 } on G such that ( G , ∘ m , ∘ n ) is a skew left brace for all m , n ≥ 0 . A brace block gives rise to a number of non-degenerate set-theoretic solutions to the Yang-Baxter equation. We give examples showing that the number of solutions obtained can be arbitrarily large.