Normal join-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
A group property 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 is said to be normal join-closed or N-closed if whenever such that and both satisfy as abstract groups, so does .