Commutator-in-center is intersection-closed
This article gives the statement, and possibly proof, of a subgroup property satisfying a subgroup metaproperty
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The property of being a commutator-in-center subgroup is an intersection-closed subgroup property: it is closed under arbitrary nonempty intersections. Note that it is not a strongly intersection-closed subgroup property because it is not closed under the empty intersection, since every group need not satisfy this property within itself.