# CS-pushforwardable automorphism

From Groupprops

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 pushforwardable automorphism|Find other variations of pushforwardable automorphism |

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

### Definition with symbols

Let be a group and an automorphism of . is said to be **CS-pushforwardable** if for any homomophism where is a characteristically simple group, there exists an inner automorphism of </math>Aut(N)</math> such that .

## Relation with other properties

### Stronger properties

- Extensible automorphism
- Semidirecty extensible automorphism
- Potentially characteristic-semidirectly extensible automorphism: The implication is a consequence of the automorphism group action lemma