Characteristic central factor

Definition
A subgroup of a group is termed a characteristic central factor if it satisfies the following two conditions:


 * It is a characteristic subgroup: every automorphism of the whole group restricts to an automorphism of the subgroup.
 * It is a central factor: every inner automorphism of the whole group restricts to an inner automorphism of the subgroup.

Stronger properties

 * Weaker than::Characteristic direct factor
 * Weaker than::Characteristic central subgroup

Weaker properties

 * Stronger than::Characteristic subgroup
 * Stronger than::Central factor
 * Stronger than::Characteristic transitively normal subgroup
 * Stronger than::Conjugacy-closed characteristic subgroup
 * Stronger than::Conjugacy-closed normal subgroup
 * Stronger than::SCAB-subgroup
 * Stronger than::Transitively normal subgroup
 * Stronger than::Normal subgroup