Modern Algebra: Finitely generated abelian groups

Exercise 10. Let A be a free abelian group with basis (a,, Q2, a3, 24). Denote by B the subgroup of A with generators bebz, by, By, where 6 = 12 a, + 24 03 + 1604 62 = - 40, + 10 02 + 20 03+ 2204 62 = 30, + 20, + Jaz + Tax 4 a + 2 0, + 4 03 + 1404 Find the orders of summands in a direct decomposition of A/ into a direct sum of infinite cyclic and cyclic p-groups