Group in which every Abelian normal subgroup is central

Symbol-free definition
A group in which every Abelian normal subgroup is central is defined as a group satisfying the following equivalent conditions:


 * Any defining ingredient::Abelian normal subgroup of the group is a defining ingredient::central subgroup, i.e., is contained in the center.
 * The center is defining ingredient::maximal among Abelian normal subgroups.

Stronger properties

 * Weaker than::Abelian group
 * Weaker than::Simple group
 * Weaker than::Fitting-free group

Weaker properties

 * Stronger than::Group in which every Abelian characteristic subgroup is central

Opposite properties

 * Group in which maximal among Abelian normal implies self-centralizing: The only groups with both these properties are the Abelian groups.