Sylow implies WNSCDIN
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., WNSCDIN-subgroup)
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Statement with symbols
Suppose is a -Sylow subgroup of a finite group , and are Normal subset (?)s of . Then, if there exists such that , there exists such that .
- Sylow implies MWNSCDIN
- Center of pronormal subgroup is subset-conjugacy-determined in normalizer
- Center of Sylow subgroup is subset-conjugacy-determined in normalizer
- Abelian Sylow implies SCDIN
- Sylow and TI implies CDIN
Proof using given facts
The proof follows directly from facts (1) and (2).