Group whose center is a direct factor

Definition
A group whose center is a direct factor is a group satisfying the following equivalent conditions:


 * 1) It is the direct product of a defining ingredient::centerless group and an defining ingredient::abelian group.
 * 2) Its defining ingredient::center is a defining ingredient::permutably complemented subgroup.
 * 3) Its center is a defining ingredient::complemented normal subgroup.
 * 4) Its center is a defining ingredient::direct factor.

Stronger properties

 * Weaker than::Abelian group
 * Weaker than::Centerless group
 * Weaker than::Simple group
 * Weaker than::Characteristically simple group
 * Weaker than::Group in which every normal subgroup is a direct factor

Weaker properties

 * Stronger than::Group whose center is an AEP-subgroup
 * Stronger than::Group having an automorphism whose restriction to the center is the inverse map

Opposite properties

 * Group whose center is normality-large
 * (non-abelian) nilpotent group