THE FORM OF AUTOMORPHISMS OF AN ABELIAN GROUP HAVING THE WEAK EXTENSION PROPERTY

Abstract

Let A be an abelian group and let α be an automorphism of A.  In this paper we show that if the restriction of α to any p-component A_p of A is of the form: α \(\upharpoonright\) A_p = πid\(_{A_{p}}\) + ρ, where p is a prime number, π a p-adic invertible number and ρ ∈ Hom(A_p, A¹) with A¹ is the first subgroup Ulm of the group A.  Then α satisfies the weak extension property.