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Math Help - order

  1. #1
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    order

    Let G be a group with |G|=6. Prove: If G is not cyclic, then G has exactly three elements of order 2.
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  2. #2
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    Quote Originally Posted by apple2009 View Post
    Let G be a group with |G|=6. Prove: If G is not cyclic, then G has exactly three elements of order 2.
    Hint: for any x in G - It's order can be 1,2,3,6. Now we have ruled out 6. (why?). So every element other than e has order 2 or 3. Now you can reason out from here.
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