Pushforwardable automorphism

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 * pushforwardable equals inner: Any pushforwardable automorphism is an inner automorphism. An automorphism $$\sigma$$ of a group $$G$$ is termed pushforwardable if, for any homomorphism $$\rho:G \to H$$, there exists an automorphism $$\sigma'$$ of $$H$$ such that $$\rho \circ \sigma = \sigma' \circ \rho$$.
 * group property-conditionally pushforwardable automorphism
 * variety-pushforwardable automorphism
 * extensible automorphisms problem discusses this and related notions.