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Direct sum

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Direct sum

I have 1 exercise. I cannot solve. Please help me solve it:

Let Q is the field of rational numbers, $ Q_p $ is the subring of Q of all rational numbers form $ frac {m} {p ^ n} $. Proved that the abel group Q / Z isomorphic to the direct sum of groups $ Q_p $ / Z


Hint: any periodic abelian group is the direct sum of its maximal p-subgroups.

By the way, I think you would be better asking your questions on math.stackexchange.com - you are likely to get more/better answers over there.

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