Image-closed intermediately subnormal-to-normal subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed image-closed intermediately subnormal-to-normal in $$G$$ if, for any surjective homomorphism $$\varphi:G \to K$$, $$\varphi(H)$$ is an defining ingredient::intermediately subnormal-to-normal subgroup of $$K$$.

This property was called strong transitively normal in a paper by Kurdachenko and Subbotin (see ).

Stronger properties

 * Weaker than::Pronormal subgroup
 * Weaker than::Weakly pronormal subgroup
 * Weaker than::Paranormal subgroup
 * Weaker than::Polynormal subgroup

Weaker properties

 * Stronger than::Intermediately subnormal-to-normal subgroup
 * Stronger than::Subnormal-to-normal subgroup