Nilpotent Hall subgroup

This article describes a property that arises as the conjunction of a subgroup property: Hall subgroup with a group property (itself viewed as a subgroup property): nilpotent group
View a complete list of such conjunctions

Definition

A subgroup of a finite group is termed a nilpotent Hall subgroup if it is a Hall subgroup (i.e., its order and index are relatively prime) and also a nilpotent group.

Relation with other properties

Stronger properties

• Abelian Hall subgroup
• Sylow subgroup

Weaker properties

• Isomorph-conjugate Hall subgroup
• Isomorph-conjugate subgroup: For full proof, refer: Nilpotent Hall implies isomorph-conjugate
• Intermediately isomorph-conjugate subgroup
• Pronormal Hall subgroup: For full proof, refer: Nilpotent Hall implies pronormal
• Procharacteristic subgroup
• Pronormal subgroup: For full proof, refer: Nilpotent Hall implies pronormal

Facts

• Nilpotent Hall subgroups of same order are conjugate