CS-pushforwardable 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)
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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
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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 </math>Aut(N)</math> such that $\phi \circ \rho =\rho \circ \sigma$ .