Perfect subnormal implies join-transitively subnormal

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., perfect subnormal subgroup) must also satisfy the second subgroup property (i.e., join-transitively subnormal subgroup)
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Statement

A perfect subnormal subgroup of a group is join-transitively subnormal: its join with any subnormal subgroup is subnormal.

Facts used

1. Perfect subnormal implies subnormal-permutable
2. Subnormality is permuting join-closed

Proof

The proof follows directly from facts (1) and (2).