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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
- Its characteristic closure in the whole group equals the whole group.
- It is not contained in any proper characteristic subgroup of the whole group.
Relation with other properties
- Every subgroup is contracharacteristic in its normal closure: In particular, every subgroup of a group is a contracharacteristic subgroup of a normal subgroup.