Sylow TI-subgroup

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

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 $p$ and the index is relatively prime to $p$.
• It is a TI-subgroup: Its intersection with any distinct conjugate subgroup is trivial.

Relation with other properties

Stronger properties

• Normal Sylow subgroup

Weaker properties

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