Right-transitively pronormal subgroup

Symbol-free definition
A subgroup of a group is termed right-transitively pronormal if every pronormal subgroup of the subgroup is pronormal in the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed right-transitively pronormal in $$G$$ if whenever $$K$$ is a pronormal subgroup of $$H$$, $$K$$ is also a pronormal subgroup of $$G$$.

Stronger properties

 * Weaker than::Direct factor
 * Weaker than::Central factor
 * Weaker than::SCAB-subgroup
 * Weaker than::Hereditarily normal subgroup
 * Weaker than::Hereditarily pronormal subgroup

Weaker properties

 * Stronger than::Pronormal subgroup