Quotient-closed group property

Symbol-free definition
A group property is said to be quotient-closed or Q-closed if any quotient of a group satisfying the property must also satisfy the property.

Definition with symbols
A group property $$p$$ is said to be quotient-closed or Q-closed if whenever $$G$$ satisfies property $$p$$, and $$N$$ is a normal subgroup of $$G$$, the quotient group $$G/N$$ must also satisfy property $$p$$.

Stronger metaproperties

 * SQ-closed group property
 * Quasivarietal group property
 * Varietal group property