Group having an abelian normal non-central subgroup

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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 having an Abelian normal non-central subgroup is a group satisfying the following equivalent conditions:

  1. There exists an Abelian normal subgroup not contained inside the center
  2. There exists an Abelian normal subgroup properly containing the center

Relation with other properties

Stronger properties