Group in which every abelian characteristic subgroup is central

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


 * Every defining ingredient::Abelian characteristic subgroup of the group is central: it is contained in the center.
 * The center is defining ingredient::maximal among Abelian characteristic subgroups: there is no Abelian characteristic subgroup properly containing the center.

Stronger properties

 * Weaker than::Abelian group
 * Weaker than::Simple group
 * Weaker than::Characteristically simple group
 * Weaker than::Fitting-free group
 * Weaker than::Group in which every Abelian normal subgroup is central

Related subgroup properties

 * Constructibly critical subgroup: A critical subgroup arising via the constructive procedure of Thompson's critical subgroup theorem automatically satisfies this condition: its center is the unique maximum among Abelian characteristic subgroups.