Extension-closed group property

This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
View a complete list of group metaproperties

Definition

Suppose $\alpha$ is a group property. We say that $\alpha$ is extension-closed if the following holds:

For any group $G$ and normal subgroup $H$ of $G$ such that both $H$ and the quotient group $G/H$ satisfy the property $\alpha$, $G$ also satisfies the property $\alpha$.

Examples

Finitely generated group, Locally finite group, Noetherian group, Periodic group, Solvable group