Sylow normalizer implies weakly abnormal

Statement
The normalizer of any Sylow subgroup in a finite group is a weakly abnormal subgroup: any subgroup containing it is a fact about::self-normalizing subgroup.

Facts used

 * 1) Sylow normalizer implies abnormal
 * 2) Abnormal implies weakly abnormal

Proof
The proof follows directly by combining facts (1) and (2).

Textbook references

 * , Page 147, Exercise 32, Section 4.5 (Sylow's theorem)