Characterization of the automorphisms of an Abelian group having the extension property (Q701344)

Let \(\alpha\) be an automorphism of an Abelian group \(A\). The authors prove that \(\alpha\) can be extended to an automorphism of any Abelian group which contains \(A\) as a subgroup if and only if \((\alpha-1_A)(A)\) or \((\alpha+1_A)(A)\) is a divisible subgroup of \(A\). Consequently, if \(A\) is reduced, \(1_A\) and \(-1_A\) are the only automorphisms of \(A\) which have the extension property.