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Showing that a subset is closed under a binary operation

  1. Feb 19, 2017 #1
    1. The problem statement, all variables and given/known data
    Suppose that * is an associative binary operation on a set S. Let ##H=\{a \in S ~| ~a*x=x*a, ~ \forall x \in S\}##. Show that * is closed under H.

    2. Relevant equations


    3. The attempt at a solution
    Let b and c be two different elements in H. We need to show that b*c is also in H.

    We know that bx = xb, and that cx = xc. Putting these two equations, and using associativity and commutativity the farthest I can get is (bc)xx = xx(bc). I'm not sure how to get (bc)x = x(bc)
     
  2. jcsd
  3. Feb 19, 2017 #2

    fresh_42

    Staff: Mentor

    You start with ##(bc)x##. And it's " H is closed under * ".
     
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