# Sylow implies WNSCDIN

From Groupprops

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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Get more facts about Sylow subgroup|Get more facts about WNSCDIN-subgroup

## Contents

## Statement

### Verbal statement

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

### 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 .

## Related facts

### Similar facts

- 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

### Opposite facts

## Facts used

## Proof

### Proof using given facts

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

### Hands-on proof

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