1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Group theory question
  1. Group theory question (Replies: 5)

  2. Group theory question (Replies: 3)

Loading...