Coprime automorphism-invariant normal subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: coprime automorphism-invariant subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a finite group is termed a coprime automorphism-invariant normal subgroup if it is both normal and coprime automorphism-invariant: it is invariant under all coprime automorphisms of the whole group.

Relation with other properties

Stronger properties

• Isomorph-normal coprime automorphism-invariant subgroup

Weaker properties

• Normal subgroup
• Coprime automorphism-invariant subgroup

Facts

• Coprime automorphism-invariant normal subgroup of Hall subgroup is normalizer-relatively normal
• Coprime automorphism-invariant normal of normal Hall implies normal
• Left residual of normal by normal Hall is coprime automorphism-invariant normal
• Hall-relatively weakly closed implies coprime automorphism-invariant normal