The Hopfian exponent of an abelian group

If $$G$$G is a Hopfian abelian group then it is, in general, difficult to determine if direct sums of copies of $$G$$G will remain Hopfian. We exhibit large classes of Hopfian groups such that every finite direct sum of copies of the group is Hopfian. We also show that for any integer $$n > 1$$n>1 there is a torsion-free Hopfian group $$G$$G having the property that the direct sum of $$n$$n copies of $$G$$G is not Hopfian but the direct sum of any lesser number of copies is Hopfian.