Nonabelian and simple subnormal subgroups of a group.

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Let $S \triangleleft \triangleleft$ $G$, where $S$ is nonabelian and simple. Show that $S^{G}$ is a minimal normal subgroup of $G$.

Notation: $S \triangleleft \triangleleft$ $G$ means $S$ is subnormal in $G$, and $S^G$ is the set $\{g^{-1}Sg:g \in G\}$.

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