  A. Smoktunowicz and L. Vendramin conjectured that if $A$ is a finite skew
brace with solvable additive group, then the multiplicative group of $A$ is
solvable. In this short note we make a step towards positive solution of this
conjecture proving that if $A$ is a minimal finite skew brace with solvable
additive group and non-solvable multiplicative group, then the multiplicative
group of $A$ is not simple. On the way to obtaining this result, we prove that
the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when
the order of $A$ is not divisible by $3$.
