Quotient-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

This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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View a list of other standard non-basic definitions


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.

Relation with other metaproperties

Stronger metaproperties