Group in which every normal-extensible automorphism is inner
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
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 normal-extensible automorphism is inner is a group wit hthe property that every normal-extensible automorphism of a group is an inner automorphism.
Formalisms
In terms of the automorphism property collapse operator
This group property can be defined in terms of the collapse of two automorphism properties. In other words, a group satisfies this group property if and only if every automorphism of it satisfying the first property (normal-extensible automorphism) satisfies the second property (inner automorphism), and vice versa.
View other group properties obtained in this way
Relation with other properties
Stronger properties
Weaker properties
- Group in which every extensible automorphism is inner
- Group in which every normal-extensible automorphism is normal