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Homework Help: Question about a group

  1. Feb 14, 2013 #1
    1. The problem statement, all variables and given/known data
    So we have this operation x*y=x+2y+4
    and then our 2nd one is x*y=x+2y-xy
    I need to check if it is commutative,associative, and if it has a identity and an inverse.
    3. The attempt at a solution
    y*x=y+2x+4 so it is not commutative

    Not associative

    Now I will solve for the identity
    Since I have 2 different identity elements this means that one does not exist because
    e should be unique.
    Since there is no e there is no inverse.

    Now for the second one x*y=x+2y-xy
    y*x=y+2x-yx Does not commute

    Not associative

    The identity element does not seem to be unique so it does not exist.
    Just want to know if I am doing this right.
  2. jcsd
  3. Feb 14, 2013 #2


    Staff: Mentor

    What do you mean "our 2nd one"? You can't define the * operation on a group in two different ways.

  4. Feb 14, 2013 #3
    The second one is just another problem. They are 2 separate problems.
  5. Feb 14, 2013 #4


    Staff: Mentor

    Then you should identify them as such instead of clumping them together as you did.
  6. Feb 14, 2013 #5


    Staff: Mentor

    What are you trying to show here? Is the exercise for each to say whether some set with the given operation is a group?

    If so, you don't need to check every group axiom for the operation. For example, if the operation isn't associative, then that's enough to say that the set and the operation aren't a group.

    Also, just because something isn't unique, that doesn't mean it doesn't exist.
  7. Feb 15, 2013 #6


    User Avatar
    Science Advisor

    More fundamentally, the identity can't depend upon "x".

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