Complemented characteristic subgroup

Symbol-free definition
A subgroup of a group is termed a complemented characteristic subgroup if it satisfies the following equivalent conditions:


 * 1) It is a defining ingredient::characteristic subgroup as well as a defining ingredient::permutably complemented subgroup.
 * 2) It is a defining ingredient::characteristic subgroup as well as a defining ingredient::lattice-complemented subgroup.
 * 3) It is a characteristic subgroup as well as a defining ingredient::complemented normal subgroup, i.e., it occurs as the normal subgroup part in an defining ingredient::internal semidirect product.

Stronger properties

 * Weaker than::Left-transitively complemented normal subgroup
 * Weaker than::Characteristically complemented characteristic subgroup
 * Weaker than::Characteristic direct factor

Weaker properties

 * Stronger than::Characteristic subgroup
 * Stronger than::Complemented normal subgroup
 * Stronger than::Permutably complemented subgroup
 * Stronger than::Lattice-complemented subgroup
 * Stronger than::Normal subgroup