# 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

### Verbal statement

Any Sylow subgroup of a finite group is a WNSCDIN-subgroup.

### Statement with symbols

Suppose $P$ is a $p$-Sylow subgroup of a finite group $G$, and $A,B \subseteq P$ are Normal subset (?)s of $P$. Then, if there exists $g \in G$ such that $gAg^{-1} = B$, there exists $k \in N_G(P)$ such that $kAk^{-1} = B$.

## Proof

### Proof using given facts

The proof follows directly from facts (1) and (2).