Complete characteristic subgroup

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


 * 1) It is complete as a group and is a characteristic subgroup of the whole group.
 * 2) It is complete as a group and is a defining ingredient::characteristic direct factor of the whole group.

Weaker properties

 * Stronger than::Characteristic direct factor
 * Stronger than::Complete direct factor
 * Stronger than::Direct factor
 * Stronger than::Characteristic subgroup
 * Stronger than::Normal subgroup