# Inner implies extensible

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., inner automorphism) must also satisfy the second automorphism property (i.e., extensible automorphism)

View all automorphism property implications | View all automorphism property non-implications

Get more facts about inner automorphism|Get more facts about extensible automorphism

## Contents

## Statement

### Verbal statement

Any inner automorphism of a group is extensible.

### Statement with symbols

Let be groups and an inner automorphism of , there is an automorphism of such that the restriction of is .

## Related facts

### Converse

## Proof

The proof in fact follows from the result:

and the fact that every inner automorphism is an automorphism.