Normality-comparable subgroup

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Definition

Symbol-free definition

A subgroup of a group is termed normality-comparable if given any normal subgroup, either the given subgroup is contained in the normal subgroup, or the normal subgroup is contained in it.

Definition with symbols

A subgroup $H$ of a group $G$ is termed normality-comparable if given any normal subgroup $N\triangleleft G$, either $N\leq H$ or $H\leq N$.

Relation with other properties

Related group properties

• Normal-comparable group: A group in which every normal subgroup is normality-comparable