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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An automorphism of a group is said to be characteristic-extensible if, for every embedding of the group as a characteristic subgroup of a bigger group, the automorphism can be extended to the bigger group.
Definition with symbols
An automorphism of a group is said to be characteristic-extensible if for any embedding of as a characteristic subgroup of a group , there exists an automorphism of such that the restriction of to is .
In terms of the qualified extensibility operator
This property is obtained by applying the qualified extensibility operator to the property: characteristicity
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The property of being a characteristic-extensible automorphism is obtained by applying the qualified extensibility operator, where the automorphism property is the tautology, and the subgroup property is that of being characteristic.