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Group theory question

  1. Jan 21, 2008 #1
    [SOLVED] group theory question

    1. The problem statement, all variables and given/known data
    A student is asked to show that if H is a normal subgroup of an abelian group G, then G/H is abelian. THe student's proof starts as follows:

    "We must show that G/H is abelian. Let a and b be two elements of G/H."

    Why does the instructor reading this proof expect to find nonsense from here on in the student's paper?

    2. Relevant equations

    3. The attempt at a solution
    That's probably how I would start my proof...I don't see anything wrong with it.
  2. jcsd
  3. Jan 21, 2008 #2
    Elements of G/H look like Hg, i.e. they are cosets of H in G. Some authors use the notation [g] = Hg to stand for the elements that are "H equivalent" to g.
  4. Jan 21, 2008 #3
    Yeah. I would have then said a must be equal to xH and b must be equal to yH, but I guess it really makes more sense to forget about a and b. Thanks.
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