---
tag: D64XR27387
kind: concept
name: Transitively normal subgroup
sources:
  - wikipedia: en:4938714@r1217768944
    locator: Transitively normal subgroup
    note: adopted
    mention: wikipedia://en/4938714
    sections: [Summary]
same_as:
  wikidata: Q7834485
  wikipedia: Transitively normal subgroup
inventory: [N980CG1NMM]
---

## Summary

In mathematics, in the field of group theory, a [[subgroup|0X1JXT47GA]] of a group is said to be **transitively normal** in the group if every [[normal subgroup|0CB0DX5BVV]] 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 $G$.