Group having no proper cocentral subgroup

Definition
A group is termed a group having no proper cocentral subgroup if the only defining ingredient::cocentral subgroup of the group is the whole group. Here, a cocentral subgroup is defined as a subgroup whose product with the center of the group is the whole group.

Opposite properties

 * Abelian group: The only abelian group satisfying this property is the trivial group. Note that for many of the properties stronger than this property, we have to explicitly include non-abelianness as a clause.