Own-variety-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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Definition

An automorphism \sigma of a group G is termed an own-variety-extensible automorphism if, for any group H containing G such that H is in the subvariety generated by G in the variety of groups, \sigma extends to an automorphism of H.

In other words, an own-variety-extensible automorphism is an automorphism of a group that satisfies the following equivalent conditions:

  • It is variety-extensible for some subvariety of the variety of groups.
  • It is variety-extensible for the subvariety of the variety of groups generated by that particular group.

Relation with other properties

Stronger properties