Direct factor of normal subgroup

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

Definition

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

• It can be expressed as a direct factor of a normal subgroup of the whole group.
• It is a direct factor inside its normal closure.

Relation with other properties

Stronger properties

• Normal subgroup
• Base of a wreath product
• Direct factor of characteristic subgroup

Weaker properties

• Central factor of normal subgroup
• 2-subnormal subgroup