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Abstract Algebra: Groups and Subgroups

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    The problem says: Suppose that * is an associative binary operation on a set S.
    Let H= {a ε S l a * x = x * a for all x ε s}. Show that H is closed under *. ( We think of H as consisting of all elements of S that commute with every element in S)

    My teacher is horrible so I am pretty lost in the class. I am aware of what the associative property is, but I'm not sure how to go about solving this question when it comes to the binary operation. This is going to be on my exam so I need to know how to solve it.
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    2. Relevant equations
    No relevant equations


    3. The attempt at a solution
    I know that with associative and groups you would try to prove its isomorphism but I'm not sure where to begin with this one
     
  2. jcsd
  3. Feb 21, 2012 #2
    No isomorphism required...

    You're just trying to show that, for any a,b[itex]\in[/itex]H, a*b[itex]\in[/itex]H. You should be able to do this with your definition of H plus associativity.
     
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