Group in which every automorphism is inner
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Definition
A group in which every automorphism is inner is a group with the property that every automorphism of the group is an inner automorphism, i.e., can be expressed via conjugation by an element.
Formalisms
In terms of the supergroup property collapse operator
This group property can be defined in terms of the collapse of two subgroup properties in the following sense. Whenever the given group is embedded as a subgroup satisfying the first subgroup property (normal subgroup), in some bigger group, it also satisfies the second subgroup property (central factor), and vice versa.
View other group properties obtained in this way