Extensible automorphism

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In mathematics, an automorphism of a structure is said to be extensible if, for any embedding of that structure inside another structure, the automorphism can be lifted to the bigger structure. In group theory, an extensible automorphism of a group is an automorphism that can be lifted to an automorphism of any group in which it is embedded. A group automorphism is extensible if and only if it is an inner automorphism, Template:Harv.

A times extensible automorphism of a group is defined inductively as an automorphism that can be lifted to a times extensible automorphism for any embedding, where a 0 times extensible automorphism is simply any automorphism. An automorphism that is times extensible for all is termed an extensible automorphism. The extensible automorphisms of a group form a subgroup for every .

Here are some properties in increasing order of generality:

References

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