Weakly characteristic subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed weakly characteristic in $$G$$ if for any $$\sigma \in \operatorname{Aut}(G)$$, $$\sigma(H) \le N_G(H)$$ implies $$\sigma(H) \le H$$. Here, $$N_G(H)$$, denotes the normalizer of $$H$$ in $$G$$.

Stronger properties

 * Weaker than::Procharacteristic subgroup
 * Weaker than::Paracharacteristic subgroup
 * Weaker than::Self-normalizing subgroup

Weaker properties

 * Stronger than::Weakly normal subgroup
 * Stronger than::Intermediately normal-to-characteristic subgroup
 * Stronger than::Intermediately subnormal-to-normal subgroup
 * Stronger than::Subgroup with self-normalizing normalizer