# Maximal Sylow intersection

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## Contents

## Definition

Let be a finite group and be a subgroup of . Let be a prime number. We say that is a **maximal -Sylow intersection** in if the following two conditions hold:

- There exist two distinct -Sylow subgroups of such that .
- For any two distinct -Sylow subgroups of , the order of is not more than the order of .