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)
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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
.