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Abelian-quotient-pullbackable automorphism
From Groupprops
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Definition
Suppose G is an abelian group and σ is an automorphism of G. We say that σ is an abelian-quotient-pullbackable automorphism of G if, for any surjective homomorphism 
from an abelian group K, there exists an automorphism σ' of K such that 
.
Relation with other properties
Related properties
- Abelian-quotient-pullbackable endomorphism
- Abelian-extensible automorphism
- Abelian-extensible endomorphism
Facts
- Free abelian group implies every automorphism is abelian-quotient-pullbackable
- Free abelian group implies every endomorphism is abelian-quotient-pullbackable
- Divisible abelian group implies every automorphism is abelian-extensible
- Divisible abelian group implies every endomorphism is abelian-extensible
