# Extensible automorphism-invariant equals normal

From Groupprops

This article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup

View a complete list of pages giving proofs of equivalence of definitions

## Contents

## Statement

The following are equivalent for a subgroup of a group:

- The subgroup is a normal subgroup: it is invariant under all inner automorphisms of the whole group.
- The subgroup is an
**extensible automorphism-invariant subgroup**: it is invariant under all extensible automorphisms of the whole group.

## Facts used

## Proof

### Conceptual proof using function restriction expressions

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