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Math Help - subgroups

  1. #1
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    subgroups

    i'm sry, please delete.. or please inform me how to..?
    Last edited by cowgirl123; October 3rd 2007 at 03:27 PM.
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  2. #2
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    Quote Originally Posted by cowgirl123 View Post
    H and K are finite subgroups of group G. |H| and |K| are relatively prime.
    Prove (H intersects K) = {identity}
    Let x\in H \mbox{ and }x\in K. Let d = \mbox{ord}(x). Then by Lagrange's theorem d|(|H|) and d|(|K|). Since these are relatively prime it means d=1. So x must be \mbox{identity}.
    Q.E.D.
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  3. #3
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    i'm not sure how this proves that the intersection of H and K is equal to the identity?
    Doesnt this just prove that the identity is in the set?
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  4. #4
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    Quote Originally Posted by cowgirl123 View Post
    i'm not sure how this proves that the intersection of H and K is equal to the identity?
    Doesnt this just prove that the identity is in the set?
    I have shown that if an element is common to both subgroups then its order must be 1. But the only element with order 1 is the identity element. Thus the identity element is the only possible element common to both.
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