Group in which maximal among abelian normal implies self-centralizing

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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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Definition

A group in which maximal among Abelian normal implies self-centralizing is a group with the following property: any subgroup that is maximal among Abelian normal subgroups is a self-centralizing subgroup.

Relation with other properties

Stronger properties

Weaker properties

If the group is non-Abelian, then it is a group having an Abelian normal non-central subgroup