Characteristic central factor

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and central factor
View other subgroup property conjunctions | view all subgroup properties

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.

Relation with other properties

Stronger properties

• Characteristic direct factor
• Characteristic central subgroup

Weaker properties

• Characteristic subgroup
• Central factor
• Characteristic transitively normal subgroup
• Conjugacy-closed characteristic subgroup
• Conjugacy-closed normal subgroup
• SCAB-subgroup
• Transitively normal subgroup
• Normal subgroup

Metaproperties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity