Divisible abelian group implies every automorphism is abelian-extensible

Statement

If $G$ is a divisible abelian group, then every automorphism of $G$ is an abelian-extensible automorphism.

Related facts

• Divisible abelian group implies every endomorphism is abelian-extensible
• Classification of abelian-extensible automorphisms, of which this can be seen as a special case.
• Classification of abelian-extensible endomorphisms
• Abelian-extensible automorphism not implies power map
• Abelian-extensible not implies normal

Facts used

1. Injective module implies every automorphism is infinity-extensible