Relatively normal subgroup

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Relatively normal subgroup, all facts related to Relatively normal subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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