Right-quotient-transitively central factor

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a right-quotient-transitively central factor if $$H$$ is a normal subgroup of $$G$$ and whenever $$K$$ is a subgroup of $$G$$ such that $$K/H$$ is a central factor of $$G/H$$, then $$K$$ is a central factor of $$G$$.

Stronger properties

 * Weaker than::Direct factor
 * Weaker than::Cocentral subgroup

Weaker properties

 * Stronger than::Join-transitively central factor:
 * Stronger than::Central factor
 * Stronger than::Transitively normal subgroup
 * Stronger than::Normal subgroup