Diagram-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 term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Definition with symbols

An automorphism \sigma of a group G is termed diagram-extensible if the following holds. Given the following data:

  • A partially ordered set I with unique minimum element 0
  • A group G_i for each i \in I such that G_0 = G
  • Inclusions G_i \to G_j for i < j, compatible with composition

There exist automorphisms \sigma_i of G_i for each i such that whenever i < j the restriction of \sigma_j to G_i is \sigma_i, and such that \sigma_0 = \sigma.

Relation with other properties

Stronger properties

Weaker properties