On the ranks of the additive and the multiplicative groups of a brace

Andrea Caranti, Ilaria Del Corso

In \cite[Theorem 2.5]{Bac16} Bachiller proved that if $(G,\cdot ,\circ )$ is a brace of order the power of a prime $p$ and the rank of $(G,\cdot )$ is smaller than $p-1$, then the o…