# Group in which every normal-extensible automorphism is inner

From Groupprops

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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 propertiesVIEW 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