Right-transitively 2-subnormal subgroup

Symbol-free definition
A subgroup of a group is termed right-transitively 2-subnormal if any defining ingredient::2-subnormal subgroup of it is 2-subnormal in the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed right-transitively 2-subnormal if whenever $$K$$ is a 2-subnormal subgroup of $$H$$, $$K$$ is also 2-subnormal in $$G$$.

Stronger properties

 * Weaker than::Base of a wreath product:
 * Weaker than::Hereditarily 2-subnormal subgroup: Also related:
 * Weaker than::Central subgroup
 * Weaker than::Abelian normal subgroup
 * Weaker than::Subgroup of abelian normal subgroup
 * Weaker than::Transitively normal subgroup: . Also related:
 * Weaker than::Direct factor
 * Weaker than::Central factor
 * Weaker than::Normal T-subgroup: A normal subgroup that is also a T-group (a group where every 2-subnormal subgroup is normal) is right-transitively 2-subnormal.
 * Weaker than::Subgroup of Dedekind normal subgroup

Weaker properties

 * Stronger than::Right-transitively fixed-depth subnormal subgroup
 * Stronger than::2-subnormal subgroup