Abelian-extensible automorphism

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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)
View other automorphism properties OR View other function properties
This term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem


Symbol-free definition

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 \sigma of an Abelian group G is termed abelian-extensible if, for any embedding of G as a subgroup of an abelian group H, there exists an automorphism \sigma' of H whose restriction to G equals \sigma.

Relation with other properties

Other related properties


Related facts