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Quick Group Question

  1. Feb 2, 2012 #1
    Lets say i have elements a,b,c,d,e in some group.


    is abcde always = ab(d^-1c^-1)e. My question is and you change elements in the middle of an operation by using the inverse?
     
  2. jcsd
  3. Feb 2, 2012 #2

    jbunniii

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    Certainly this is not true. Take your equation and cancel the a, b, and e by multiplying on the appropriate side by the appropriate inverse in each case. You are left with

    cd = (d^-1 c^-1)

    and the right hand side is equal to (cd)^-1.

    Obviously in general, cd does not equal its own inverse, so the equation is false.
     
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