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
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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
- Conjugacy-closed normal subgroup
- Transitively normal subgroup
- Characteristic subgroup
- Characteristic transitively 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.
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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).
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