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)
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- 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
- Sylow implies order-conjugate: This is the conjugacy part of Sylow's theorem.
- Order-conjugate implies isomorph-conjugate
The proof follows directly from facts (1) and (2).