Let $\kappa$ be an inaccessible cardinal, and let $G$ be a group with $|G| \geq \kappa$. For any cardinal $\lambda \le \kappa$ (regular, say, but not necessary), say $G$ is $\lambda$-simple if for all normal subgroups $N \lt G$ we have $|N| \le \lambda$. Clearly a group is simple iff it is $2$-simple. Can we force (or even construct without forcing) a $\lambda$-simple group $G$?