Subgroup realizable as the commutator of the whole group and a subgroup

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]

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Definition

A subgroup of a group is termed realizable as the commutator of the whole group and a subgroup if it can be realized as the commutator of the whole group and a subgroup.

Relation with other properties

Stronger properties

• Perfect normal subgroup
• Member of the (finite) lower central series

Weaker properties

• Subgroup realizable as the commutator of two subgroups
• Normal subgroup: For full proof, refer: Commutator of the whole group and a subgroup implies normal