Direct factor of normal subgroup

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 defining ingredient::normal closure.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Base of a wreath product
 * Weaker than::Direct factor of characteristic subgroup

Weaker properties

 * Stronger than::Central factor of normal subgroup
 * Stronger than::2-subnormal subgroup
 * Stronger than::Subnormal subgroup