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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.

Contents 1 In terms of being able to extend to bigger groups 1.1 Extensible automorphism 1.2 Pushforwardable automorphism 1.3 Quotient-pullbackable automorphism 2 Definition in terms of universal algebra 2.1 I-automorphism

In terms of being able to extend to bigger groups

Extensible automorphism

Further information: Extensible equals inner, Inner implies extensible

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

Pushforwardable automorphism

Further information: Pushforwardable equals inner

An automorphism σ < math > ofagroup < math > G is termed inner if it is a pushforwardable automorphism: For any homomorphism of groups , there is an automorphism of H such that .

Quotient-pullbackable automorphism

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

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

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.