2-hypernormalized subgroup

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

Symbol-free definition

A subgroup of a group is termed 2-hypernormalized if its normalizer is a normal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup

Weaker properties

• Finitarily hypernormalized subgroup
• 2-subnormal subgroup
• Hypernormalized subgroup
• Subnormal subgroup
• Conjugate-permutable subgroup