# Abelian implies every element is automorphic to its inverse

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., abelian group) must also satisfy the second group property (i.e., group in which every element is automorphic to its inverse)

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## Statement

Suppose is an abelian group. Then, for any , there is an automorphism sending to .

## Facts used

## Proof

The proof follows from fact (1).