In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (An) is considered, where A0 = A and An+1 = End An. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A0 or after A1.