Extension-closed group property

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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