abstract algebra: G abelian, finite, of order o(G), w/ (n, o(G)) = 1, then prove:

[mohammad2232]

Hello. I have a question from abstract algebra:

If G is abelian, finite, and with o(G) degree, and if n is integral number and (n,o(G)) = 1, then prove the following:

For all g in G, there exists one x in G such that g = x^n.

Thanks very much for your time

 

[Deleted member 4993]

helloi have a question from abstract algebraif G is abelian and finite and with o(G) degree and n is integral number and (n,o(G))=1 then prove that:for all g in G exists one x in G ; g=x^nthanks very much for your time

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[mohammad2232]

thanks

Let m = o(G) , g = g^1= g^(np+mq)=(g^p)^n , g is finite ang g^o(G)=e and e^b=e and for continue we can say g^p is a one exist for example name x and final say g=(g^p)^n=x^nthis is true ? thanks