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.

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:

• Every normal subgroup of a transitively normal subgroup is normal.

• Every direct factor, or more generally, every central factor is transitively normal. Thus, every central subgroup is transitively normal.

• A transitively normal subgroup of a transitively normal subgroup is transitively normal.

• A transitively normal subgroup is normal.

References

See also

• Normal subgroup