Group in which every abelian characteristic subgroup is central
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A group in which every Abelian characteristic subgroup is central is a group satisfying the following equivalent conditions:
- Every Abelian characteristic subgroup of the group is central: it is contained in the center.
- The center is maximal among Abelian characteristic subgroups: there is no Abelian characteristic subgroup properly containing the center.
Relation with other properties
- Abelian group
- Simple group
- Characteristically simple group
- Fitting-free group
- Group in which every Abelian normal subgroup is central