Hall subgroup of normal subgroup

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: Hall subgroup and normal subgroup
View other such compositions|View all subgroup properties

Definition

A subgroup of a finite group is termed a Hall subgroup of normal subgroup if it can be expressed as a Hall subgroup of a normal subgroup.

Relation with other properties

Stronger properties

• Intersection of Hall subgroup and normal subgroup
• Sylow subgroup of normal subgroup

Weaker properties

• Paranormal subgroup
• Polynormal subgroup
• Intermediately subnormal-to-normal subgroup

Metaproperties

Intermediate subgroup condition

YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition