For arbitrary natural numbers a and b, I don't think the direct sum of Z_a and Z_b (considered as additive groups) is isomorphic to Z_ab. But I think if p and q are distinct primes, the direct sum of Z_p^m and Z_q^n is always isomorphic to Z_(p^m * q^n). Am I right? I've been freely using these facts in abstract algebra, but I wanted to make sure they're correct.(adsbygoogle = window.adsbygoogle || []).push({});

Any help would be greatly appreciated.

Thank You in Advance.

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# Is the direct sum of cyclic p-groups a cyclic group?

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