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Weakly closed subgroup

This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
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Suppose H \le K \le G. Then, H is termed weakly closed in K relative to G if, for any g \in G such that gHg^{-1} \le K, we have gHg^{-1} \le H.

There is a related notion of weakly closed subgroup for a fusion system.

Relation with other properties