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Math Help - Groups

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    33

    Groups

    Hey, I am not entirely sure if I am doing this right. But anyways...
    The directions say...

    "Determine whether the binary operation * defined on the given set results in a group."
    (A group is classified by 3 properties:
    Associative Law a * (b * c) = (a * b) * c
    Existence of an Identity: There exists an element, e, such that
    a * e = e * a = a
    Existence of Inverses: For each element, a, there exists an element, s,
    such that a * s = s * a = e (the identity)

    So, here is what I'm supposed to do:

    (a) Let * be defined on the positive reals by a * b= √(ab)

    (b) Let * be defined on all the Reals except 0, by a * b= a/b

    (c) Let * be defined on all the Reals except 0, by a * b= a+b+ab


    Any help would be much appreciated!
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  2. #2
    Member
    Joined
    Dec 2008
    From
    Indiana
    Posts
    127
    Quote Originally Posted by dude15129 View Post
    Hey, I am not entirely sure if I am doing this right. But anyways...
    The directions say...

    "Determine whether the binary operation * defined on the given set results in a group."
    (A group is classified by 3 properties:
    Associative Law a * (b * c) = (a * b) * c
    Existence of an Identity: There exists an element, e, such that
    a * e = e * a = a
    Existence of Inverses: For each element, a, there exists an element, s,
    such that a * s = s * a = e (the identity)

    So, here is what I'm supposed to do:

    (a) Let * be defined on the positive reals by a * b= √(ab)

    (b) Let * be defined on all the Reals except 0, by a * b= a/b

    (c) Let * be defined on all the Reals except 0, by a * b= a+b+ab


    Any help would be much appreciated!
    Hi,

    (a) Yes.

    (b) No. Associativity fails.

    (c) No. The identity element does not exist.

    See if you can come up with the detailed work.
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  3. #3
    Junior Member
    Joined
    Aug 2008
    Posts
    33
    Awesome...Those were actually what I was thinking, but I wasn't really sure. Thanks so much!
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