# Sylow TI-subgroup

From Groupprops

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: Sylow subgroup and TI-subgroup

View other subgroup property conjunctions | view all subgroup properties

## Contents

## Definition

A subgroup of a finite group is termed a **Sylow TI-subgroup** or a **TI Sylow subgroup** if it satisfies the following conditions:

- It is a Sylow subgroup: Its order is a power of a prime and the index is relatively prime to .
- It is a TI-subgroup: Its intersection with any distinct conjugate subgroup is trivial.

## Relation with other properties

### Stronger properties

### Weaker properties

- Sylow CDIN-subgroup:
`For full proof, refer: Sylow and TI implies CDIN`