Coprime automorphism-faithful normal subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: coprime automorphism-faithful subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition
Symbol-free definition
A subgroup of a group is termed a coprime automorphism-faithful normal subgroup if it is both a coprime automorphism-faithful subgroup and a normal subgroup of the whole group.
Relation with other properties
Stronger properties
- Self-centralizing normal subgroup: For full proof, refer: Normal and self-centralizing implies coprime automorphism-faithful
- Coprime automorphism-faithful characteristic subgroup
- Automorphism-faithful normal subgroup
- Automorphism-faithful characteristic subgroup
- Centralizer-free normal subgroup
- Centralizer-free characteristic subgroup