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Math Help - cyclic group

  1. #1
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    cyclic group

    Show that < Z(mod2) X Z(mod3), +> is a cyclic group. The Z's have 2 and 3 has subscripts...
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    Show that < Z(mod2) X Z(mod3), +> is a cyclic group. The Z's have 2 and 3 has subscripts...


    Hint - Lemma: if x,y are two elements of finite coprime order in a group and they commute (i.e., xy=yx), then ord(xy)=ord(x)ord(y)

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