FROM BRACES TO PRE-LIE RINGS

Let A be a brace of cardinality p(n) where p > n + 1 is prime and let ann(p(2)) be the set of elements of additive order at most p(2) in this brace. We construct a pre-Lie ring related to the brace A/ann(p(2)). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p(2)) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.