Single-witness EAC-true group

Definition
A group $$G$$ is termed a single-witness EAC-true group if there exists a group $$H$$ containing $$G$$ such that any automorphism of $$G$$ that extends to an automorphism of $$H$$ is an inner automorphism of $$G$$.

Stronger properties

 * Weaker than::Complete group
 * Weaker than::Group in which every automorphism is inner

Weaker properties

 * Stronger than::EAC-true group