# Sylow-permutable implies subnormal in finite

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite group. That is, it states that in a Finite group (?), every subgroup satisfying the first subgroup property (i.e., Sylow-permutable subgroup (?)) must also satisfy the second subgroup property (i.e., Subnormal subgroup (?)). In other words, every Sylow-permutable subgroup of finite group is a subnormal subgroup of finite group.

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## Statement

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