Perfect subnormal implies subnormal-permutable
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., subnormal-permutable subgroup)
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Any perfect subnormal subgroup of a group is subnormal-permutable: it permutes with any subnormal subgroup of the whole group. Thus, any perfect subnormal subgroup is a subnormal-permutable subnormal subgroup.