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