posed by Drinfeld [@drinfeld], Rump in [@Rump] introduced the new algebraic object, called a left brace. A left brace $(B,+,\cdot)$ is a set $B$ with two operations, $+$ and $\cdot$, such that $(B,+)$ is an abelian group, $(B,\cdot)$ is a group and $a\cdot (b+c)+a=a\cdot b+a\cdot c$ for all $a,b,c\in B$. Braces have been shown to appear in an intriguing way in several areas of mathematics, see the surveys [@Rump7; @C18]. The class of set-theoretic solutions of the Yang-Baxter equation that are involutive and non-degenerate has received a lot of attention in recent years, see for example [@CJO2; @CJR; @ESS; @GI; @GIC; @GIVdB; @Ven1; @JObook; @Rump1; @Rump]. It has been shown that all such finite solutions can be obtained, in a constructive way, from a description of all finite left braces [@BCJ]. It thus is a fundamental problem to classify the building blocks in the class of all finite left braces, i.e. describe all finite simple left braces. For finite left braces with nilpotent multiplicative group, such objects are precisely the cyclic groups of prime order, with the operations $\cdot$ and $+$ coinciding (see [@Rump Corollary on page 166] and [@B3 Proposition 6.1]). Attacking the classification problem from another perspective, Rump 