Normal Sylow subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and Sylow subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a finite group is termed a normal Sylow subgroup if it satisfies the following equivalent conditions:

• It is a Sylow subgroup, and is normal in the whole group.
• It is a Sylow subgroup, and is subnormal in the whole group.
• It is a Sylow subgroup, and is characteristic in the whole group.
• It is a Sylow subgroup, and is fully characteristic in the whole group.

Relation with other properties

Weaker properties

• Nilpotent normal subgroup
• Nilpotent characteristic subgroup
• Normal Hall subgroup
• Complemented normal subgroup
• Fully characteristic subgroup
• Characteristic subgroup
• Intermediately characteristic subgroup
• Isomorph-free subgroup
• Intermediately fully characteristic subgroup
• Image-closed characteristic subgroup
• Image-closed fully characteristic subgroup
• Normal subgroup