Transitively normal subgroup

In mathematics, in the field of group theory, a subgroup of a group is said to be transitively normal in the group if every normal subgroup of the subgroup is also normal in the whole group. In symbols, H is a transitively normal subgroup of G if for every K normal in H , we have that K is normal in G .

An alternate way to characterize these subgroups is: every normal subgroup preserving automorphism of the whole group must restrict to a normal subgroup preserving automorphism of the subgroup.

Here are some facts about transitively normal subgroups: