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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This term is related to: Extensible automorphisms problem
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An automorphism of an abelian group is termed abelian-extensible if it can be extended to an automorphism for any embedding of the group in an abelian group.
Definition with symbols
An automorphism of an Abelian group is termed abelian-extensible if, for any embedding of as a subgroup of an abelian group , there exists an automorphism of whose restriction to equals .
Relation with other properties
- Divisible abelian group implies every automorphism is abelian-extensible
- Abelian-extensible automorphism not implies power map
- Subgroup of abelian group not implies abelian-extensible automorphism-invariant