Characterization of the automorphisms of an abelian torsion group having the weakly extension property

In this paper, we show that if an automorphism α of an abelian torsion group, which is in fact a direct sum of its p  -components, has the weak extension property then α=πidAp+ρα=πidAp+ρ, where p is a prime number, π is an invertible p  -adic number and ρ∈Hom(Ap,Ap1) with Ap1 is the first Ulm subgroup of the p-component Ap of A.