Solvable-extensible automorphism

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 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]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Solvable-extensible automorphism, all facts related to Solvable-extensible automorphism) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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 $G</ma/th>inasolvablegroup<math>H$, there exists an automorphism $\varphi$ of $H$ whose restriction to $G$ is $\sigma$.

Relation with other properties=

Stronger properties

• Extensible automorphism when the underlying group is solvable

Weaker properties

• Nilpotent-extensible automorphism when the underlying group is nilpotent