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Math Help - Group Axioms G4 Associative

  1. #1
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    Group Axioms G4 Associative

    Hi!

    Could anyone help!

    I need to prove G4 associativity for the following group and I know it exists

    (Q*, o) where x o y = xy/7.

    This group is closed so G1 holds
    This group is has an identity e = 7 so G2 holds
    This group has an inverses which is 49/x.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Arron View Post
    Hi!

    Could anyone help!

    I need to prove G4 associativity for the following group and I know it exists

    (Q*, o) where x o y = xy/7.

    This group is closed so G1 holds
    This group is has an identity e = 7 so G2 holds
    This group has an inverses which is 49/x.
    Associativity is the `easy' one, because you don't really have to think! All you have to do is calculate (x \circ y) \circ z and x \circ (y \circ z) and see if they are the same!

    So...do this...
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  3. #3
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    Thanks. I assume you mean the following.


    x o (y o z) = x/7 o (yz/7)
    = xyz/49

    (x o y) o z = 1/7(xy/7) o z
    = xyz/49
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  4. #4
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Arron View Post
    Thanks. I assume you mean the following.


    x o (y o z) = x/7 o (yz/7)
    = xyz/49

    (x o y) o z = 1/7(xy/7) o z
    = xyz/49
    Not quite - x \circ (y\circ z) = x\circ \frac{yz}{7} - you put in the "/7" as you perform the multiplication, and similarly with the other part.
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