Sylow implies isomorph-conjugate
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., Sylow subgroup) must also satisfy the second subgroup property (i.e., isomorph-conjugate subgroup)
View all subgroup property implications | View all subgroup property non-implications
Get more facts about Sylow subgroup|Get more facts about isomorph-conjugate subgroup
Statement
Any Sylow subgroup of a finite group is an isomorph-conjugate subgroup: it is conjugate to any isomorphic subgroup.
Related facts
Applications
- Sylow implies intermediately isomorph-conjugate
- Sylow implies automorph-conjugate
- Sylow implies intermediately automorph-conjugate
- Sylow implies procharacteristic
- Sylow implies pronormal
- Sylow of normal implies pronormal
Facts used
- Sylow implies order-conjugate: This is the conjugacy part of Sylow's theorem.
- Order-conjugate implies isomorph-conjugate
Proof
The proof follows directly from facts (1) and (2).