# Conjugation-invariantly relatively normal subgroup

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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.

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## Definition

Suppose . We say that is **conjugation-invariantly relatively normal** in with respect to if is a normal subgroup in every conjugate of in that contains .

## Relation with other properties

### Stronger properties

- Strongly closed subgroup
- Weakly closed subgroup:
*For proof of the implication, refer Weakly closed implies conjugation-invariantly relatively normal and for proof of its strictness (i.e. the reverse implication being false) refer Conjugation-invariantly relatively normal not implies weakly closed*.