Left residual-preserved subgroup metaproperty

Definition
A subgroup metaproperty $$\alpha$$ is termed left residual-preserved if given subgroup properties $$p,q$$ such that $$p$$ satisfies $$\alpha$$, the left residual of $$p$$ by $$q$$ also satisfies $$\alpha$$.

Weaker metaproperties

 * Stronger than::Left transiter-preserved subgroup metaproperty