On the triviality and non-triviality of the automorphism group of a skew brace

Abstract: It is a simple fact that a group has a trivial automorphism group if and only if it is of order $1$ or $2$. We prove that the same holds for certain families of skew braces, and given any odd prime $p$, we construct a skew brace of order $2p^3$ that has a trivial automorphism group.