Complete direct factor

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


 * 1) It is both a complete group (as a group by itself) and a normal subgroup of the whole group.
 * 2) It is both a complete group (as a group by itself) and a direct factor of the whole group.
 * 3) It is both a complete group (as a group by itself) and a defining ingredient::complemented normal subgroup  of the whole group.

Stronger properties

 * Weaker than::Complete characteristic direct factor

Weaker properties

 * Stronger than::Direct factor
 * Stronger than::Normal subgroup of complete direct factor