P-normal-extensible automorphism-invariant 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

A subgroup of a p-group is termed a p-normal-extensible automorphism-invariant subgroup if it is invariant under all the p-normal-extensible automorphisms of the whole group.

Relation with other properties

Stronger properties

• Characteristic subgroup of p-group
• Normal-extensible automorphism-invariant subgroup of p-group

Weaker properties

• Normal subgroup of p-group