# CS-pushforwardable 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)
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

## Contents

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

## Definition

### Definition with symbols

Let $G$ be a group and $\sigma$ an automorphism of $G$. $\sigma$ is said to be CS-pushforwardable if for any homomophism $\rho:G \to Aut(N)$ where $N$ is a characteristically simple group, there exists an inner automorphism $\phi$ of [/itex]Aut(N)[/itex] such that $\phi \circ \rho = \rho \circ \sigma$.