Groupprops, The Group Properties Wiki (pre-alpha)
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Group property-conditionally extensible automorphism
From Groupprops
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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This term is related to: extensible automorphisms problem
View other terms related to extensible automorphisms problem | View facts related to extensible automorphisms problem
Definition
Suppose α is a group property and G is a group satisfying α. An automorphism σ of G is termed extensible with respect to α, or extensible conditional to α, if for any group H containing G such that H satisfies property α, there is an automorphism σ' of H whose restriction to G equals σ.
For more information on the best known results and characterization, refer extensible automorphisms problem.
When the groups satisfying α form a subvariety of the variety of groups, this is equivalent to the notion of variety-extensible automorphism for that subvariety.
Also note that any inner automorphism is conditionally extensible with respect to any group property.
Relation with other properties
Stronger properties
Related properties
Other related notions
- Variety-extensible automorphism
- Own variety-extensible automorphism
- Extensibility operator
- Qualified extensibility operator
