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.
View other such properties

Definition

Suppose $H \le K \le G$ are groups. We say that $H$ is relatively normal in $K$ with respect to $G$ if $H$ is a normal subgroup of $K$.

Relation with other properties

Stronger properties

• Absolutely normal subgroup
• Strongly closed subgroup
• Weakly closed subgroup
• Conjugation-invariantly relatively normal subgroup