Centerless group that is upward-closed normal in its automorphism 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 centerless group that is upward-closed normal in its automorphism group is defined as follows: it is a centerless group, and when it is embedded inside its automorphism group via the action by conjugation, every subgroup of the automorphism group containing it, is a normal subgroup of the automorphism group.

Relation with other properties

Stronger properties