Perfect subnormal implies subnormal-permutable

Statement
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.

Facts used

 * 1) uses::Orthogonal subnormal subgroups permute

Proof
The proof follows from fact (1), and the observation that a perfect group is orthogonal to any group.