Solvable-extensible automorphism

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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 is a variation of extensible automorphism|Find other variations of extensible automorphism |
This term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

Symbol-free definition

An automorphism of a solvable group is said to be solvable-extensible if it can be extended to an automorphism for any embedding of the given solvable group in a solvable group.

Definition with symbols

Let G be a solvable group and \sigma an automorphism of G. Then \sigma is said to be solvable-extensible if for any embedding of G</ma/th> in a solvable group <math>H, there exists an automorphism \phi of H whose restriction to G is \sigma.

Relation with other properties=

Stronger properties

Weaker properties