Sylow implies pronormal
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 subgroup (?)) must also satisfy the second subgroup property (i.e., Pronormal subgroup (?)). In other words, every Sylow subgroup of finite group is a pronormal subgroup of finite group.
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Further information: Sylow subgroup
Further information: Pronormal subgroup
- Sylow normalizer implies abnormal
- Sylow normalizer implies upward-closed self-normalizing
- Sylow implies intermediately subnormal-to-normal
The proof follows directly by combining facts (1) and (2).