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Homework Statement
If G is a finite abelian group that has one subgroup of order d for every divisor d of the order of G. Prove that G is cyclic.
I think the point is that it is supposed to have ONE subgroup of each order. Your example has several subgroups of order 2.Can you check the question. C_2 x C_2 has subgroups of orders 1,2 and 4, but is not cyclic.