It seems rather straight forward that if you have an abelian group G with [itex]\# G = p_1 p_2 \cdots p_n [/itex] (these being(adsbygoogle = window.adsbygoogle || []).push({}); differentprimes), that it is cyclic. The reason being that you have elements [itex]g_1, g_2, \cdots g_n[/itex] with the respective prime order (Cauchy's theorem) and their product will have to have the order of G. Rather simple, but I wanted to check that I'm not overlooking something simple because I find the result rather interesting although I was never told this in any of my algebra classes, which strikes me as strange.

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# Abelian group with order product of primes = cyclic?

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