Transitively Normal Subgroup
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.