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Math Help - Cyclic Groups

  1. #1
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    Cyclic Groups

    Let G1 and G2 be groups, and let f: G1 -> G2 be an isomorphism.
    If G1 is a cyclic group with generator a, prove that G2 is also a cyclic group, with generator f(a).

    Can someone show this proof? Thanks so much!!
    Last edited by jzellt; October 31st 2010 at 11:13 PM.
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  2. #2
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    I believe you mean the generator to be f(a). Here's a hint: any element in the first group can be represented as a^n for some integer n. Now given an element in the second group (say b), we can express b = f(a^n). Can you figure out the rest?
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