On bi-skew braces and brace blocks

L. N. Childs defined a bi-skew brace to be skew such that if we swap the role of two operations, then find again brace. In this paper, give systematic analysis braces. We study nilpotency and solubility, connections between braces set-theoretic solutions Yang–Baxter equation. Further, deal with Byott's conjecture in case braces, use as tool solve classification problem proposed by Vendramin. final part, investigate blocks, A. Koch families group operations on given set any them yield provide characterisation illustrate how all known constructions literature follow natural way from our characterisation, several new examples.