Holomorph-characteristic group

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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 is termed a holomorph-characteristic group if it is a characteristic subgroup inside its holomorph of a group.

Relation with other properties

Stronger properties

• Odd-order cyclic group: For full proof, refer: Odd-order cyclic group is characteristic in holomorph
• Additive group of a field, Elementary abelian group: For full proof, refer: Additive group of a field implies characteristic in holomorph