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Groupprops β

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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Contents

Statement

Definitions used

Sylow subgroup

Further information: Sylow subgroup

Pronormal subgroup

Further information: Pronormal subgroup

Related facts

Facts used

Proof

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