Nonstandard definitions of inner automorphism

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This article lists nonstandard definitions of the following term: inner automorphism

This page lists some offbeat, but correct, definitions of inner automorphism.

In terms of being able to extend to bigger groups

Extensible automorphism

Further information: Extensible equals inner, Inner implies extensible

An automorphism \sigma of a group G is termed inner if it is an extensible automorphism: For any group K containing G, \sigma extends to an automorphism of K.

Pushforwardable automorphism

Further information: Pushforwardable equals inner

An automorphism \sigma of a group G is termed inner if it is a pushforwardable automorphism: For any homomorphism of groups \rho:G \to H, there is an automorphism \varphi of H such that \rho \circ \sigma = \varphi \circ \rho.

Quotient-pullbackable automorphism

Further information: Quotient-pullbackable equals inner, Inner implies quotient-pullbackable

An automorphism \sigma of a group G is termed inner if it is a quotient-pullbackable automorphism: For any surjective homomorphism \rho:K \to G, there exists an automorphism \sigma' of K such that \rho \circ \sigma' = \sigma \circ \rho.

Definition in terms of universal algebra

I-automorphism

Further information: Inner automorphisms are I-automorphisms in the variety of groups

An automorphism of a group is termed an inner automorphism if it is an I-automorphism in the variety of groups.