Normal join-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

Symbol-free definition

A group property p is said to be normal join-closed or N-closed if it satisfies the following. Whenever there are two normal subgroups of a group, both having the property as abstract groups, then their join also has the property as an abstract group.

Definition with symbols

A group property p is said to be normal join-closed or N-closed if whenever N_1, N_2 \triangleleft G such that N_1 and N_2 both satisfy p as abstract groups, so does N_1N_2.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties