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

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 {o(n) : n is an element of Z(>= 0)} on G such that (G, o(m), o(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.(c) 2022 Elsevier B.V. All rights reserved.