NSCFN-subgroup

Symbol-free definition
A subgroup of a group is termed a NSCFN-subgroup if it is normal, fully normalized and self-centralizing in the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a NSCFN-subgroup if $$H \triangleleft G$$, $$H$$ is fully normalized in $$G$$, and $$C_G(H) \le H$$.

Equivalently, $$H$$ is a NSCFN-subgroup of $$G$$ if $$H$$ is a normal subgroup of $$G$$, and the induced homomorphism $$G \to \operatorname{Aut}(H)$$ induced by the conjugation action is surjective with kernel equal to $$Z(H)$$.