# Transitive normality is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., transitively normal subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about transitively normal subgroup |Get facts that use property satisfaction of transitively normal subgroup | Get facts that use property satisfaction of transitively normal subgroup|Get more facts about transitive subgroup property

## Statement

Suppose are groups, such that is a transitively normal subgroup of and is a transitively normal subgroup of , then is a transitively normal subgroup of .