Sylow-permutable implies subnormal in finite

Statement
In a finite group, any Sylow-permutable subgroup (i.e., any subgroup that permutes with all Sylow subgroups) is subnormal.

Related facts

 * Conjugate-permutable implies subnormal in finite

Facts used

 * 1) uses::Sylow-permutability satisfies intermediate subgroup condition
 * 2) uses::Maximal Sylow-permutable implies normal