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Math Help - group theory proof

  1. #1
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    group theory proof

    Let G be a group

    if the order(g) = 2 for all g then prove G is abelian

    My proof:

    order(g) = 2

    g^2 = e
    g.g(^-1) = e

    g.g = g.g(^-1)

    therefore g= g^-1

    g.g(^-1) = g^2 = e = g(^-1).g

    therefore G is abelian

    my proof is dont look right

    HELP PLEASE!!!
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  2. #2
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    Quote Originally Posted by Dreamer78692 View Post
    Let G be a group

    if the order(g) = 2 for all g then prove G is abelian

    My proof:

    order(g) = 2

    g^2 = e
    g.g(^-1) = e

    g.g = g.g(^-1)

    therefore g= g^-1

    g.g(^-1) = g^2 = e = g(^-1).g

    therefore G is abelian

    my proof is dont look right

    HELP PLEASE!!!

    Your "proof" doesn't look right because you didn't prove anything close to what you were asked: you

    only "proved" that g=g^{-1}\,\,and\,\,gg^{-1}=e\,,\,\,\forall g\in G , the former being

    a rather obvious property in this kind of groups, and the latter being an axiom of group theory.

    What you have to prove is: \forall x,y \in G\,,\,xy=yx . Hint: use that (xy)^2=e\,\,and\,\,also\,\,x=x^{-1}

    Tonio
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  3. #3
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    Thanks... i get how to do it
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