On the multiplicative group of a two-sided skew brace of solvable type

We prove that if $(B,+,\cdot )$ is a two-sided skew brace whose additive group is solvable, then every finite quotient of the multiplicative group $(B,\cdot )$ is solvable. In particular, our result recovers Nasybullov’s theorem in the finite case ~\cite[Theorem~4.3(1)]{Nas} and extends it to arbitrary two-sided skew braces of solvable type.