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) uses::Injective module implies every automorphism is infinity-extensible