Nilpotent-extensible automorphism

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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 extensible automorphism|Find other variations of extensible automorphism |
This term is related to: Extensible automorphisms problem
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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Symbol-free definition

An automorphism of a nilpotent group is said to be nilpotent-extensible if it can be extended to an automorphism for every embedding of the given nilpotent group into a nilpotent group.

Definition with symbols

Let G be a nilpotent group and \sigma an automorphism of G. Then we say that \sigma is nilpotent-extensible if for any embedding of G in a nilpotent group H, there is an automorphism \phi of H such that the restriction of \phi to G is \sigma.

Relation with other properties

Stronger properties