Centralizer-free normal subgroup

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

Definition

A subgroup of a group is termed a centralizer-free normal subgroup if it is both a centralizer-free subgroup of the whole group and a normal subgroup of the whole group.

Relation with other properties

Weaker properties

• Automorphism-faithful subgroup: For full proof, refer: Normal and centralizer-free implies automorphism-faithful
  • Automorphism-faithful normal subgroup