Group in which every Abelian normal subgroup is central
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A group in which every Abelian normal subgroup is central is defined as a group satisfying the following equivalent conditions:
- Any Abelian normal subgroup of the group is a central subgroup, i.e., is contained in the center.
- The center is maximal among Abelian normal subgroups.
Relation with other properties
- Group in which maximal among Abelian normal implies self-centralizing: The only groups with both these properties are the Abelian groups.