Abelian direct factor

Definition
A subgroup of a group is an abelian direct factor or central direct factor or complemented central subgroup if it satisfies the following conditions:


 * 1) It is abelian as a group and is a direct factor of the whole group.
 * 2) It is both a central subgroup and a direct factor of the whole group.
 * 3) It is both a central subgroup and a conjunction involving::permutably complemented subgroup of the whole group.
 * 4) It is both a central subgroup and a conjunction involving::complemented normal subgroup of the whole group.
 * 5) It is both a central subgroup and a conjunction involving::complemented central factor of the whole group.
 * 6) It is both a central subgroup and a conjunction involving::lattice-complemented subgroup of the whole group.