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Math Help - Preserving structural properties

  1. #1
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    Preserving structural properties

    Prove that if G′ is cyclic then so is G.



    Thanks for the help!
    Last edited by Kiwili49; October 22nd 2009 at 09:33 PM. Reason: Done with proof
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  2. #2
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    Let f(a)=b \in G' be a generator for G' with a \in G. Since every y \in G' is of the form b^n for some n we have y=b^n=f(a)^n=f(a^n) ie. every element in the image of f comes from some a^n, since f is one-one we conclude that every element in G is of the form a^n which means G is cyclic
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