# 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, ${\displaystyle H}$ is a transitively normal subgroup of ${\displaystyle G}$ if for every ${\displaystyle K}$ normal in ${\displaystyle H}$, we have that ${\displaystyle K}$ is normal in ${\displaystyle G}$.