Inner-in-automorphism-Frattini 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 an inner-in-automorphism-Frattini group if its inner automorphism group is a Frattini-embedded normal subgroup of its automorphism group.

Relation with other properties

Stronger properties

• Finite-Frattini-realizable group
• Frattini-embedded normal-realizable group: For full proof, refer: Frattini-embedded normal-realizable implies inner-in-automorphism-Frattini

Weaker properties

• ACIC-group: For full proof, refer: Inner-in-automorphism-Frattini implies ACIC