# Powering-invariance is strongly intersection-closed

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., powering-invariant subgroup) satisfying a subgroup metaproperty (i.e., strongly intersection-closed subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

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## Statement

Suppose is a group, is an indexing set, and is a collection of powering-invariant subgroups of . Then, the intersection of subgroups is also a powering-invariant subgroup of .