Middle-characteristic subgroup

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 $H\leq K\leq G$ are groups. We say that $H$ is middle-characteristic if $H$ is a characteristic subgroup of $K$.

Relation with other properties

Stronger properties

• Relatively characteristic subgroup

Weaker properties

• Normalizer-relatively normal subgroup
• Relatively normal subgroup