Conjugacy-closed characteristic subgroup

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

Definition

A subgroup of a group is termed a conjugacy-closed characteristic subgroup if it is both a conjugacy-closed subgroup (i.e., any two elements of the subgroup that are conjugate in the whole group are conjugate in the subgroup) and a characteristic subgroup.

Relation with other properties

Stronger properties

• Characteristic direct factor
• Characteristic central factor

Weaker properties

• Conjugacy-closed normal subgroup
• Transitively normal subgroup
• Characteristic subgroup
• Characteristic transitively 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

Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties