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Anstract Algebra proof - cosets

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Let H be a subgroup of G such that g^-1hg is an element of H for all g in G and all h in H. Show that every left coset gH is the same as the right coset Hg.


    2. Relevant equations



    3. The attempt at a solution
    need to show gh1=h2g
    I know I need to show this, but am unsure on how to.
     
  2. jcsd
  3. Apr 27, 2009 #2
    I know the whole set up excpet for this part and it confuses me.
     
  4. Apr 27, 2009 #3
    Let g be in G, h in H (sorry, Latex seems to be failing presently). As you say, you need to show that there exists k in H such that
    gh = kg. You know that ghg-1 = k is in H. Rearrange this to get something useful.
     
  5. Apr 28, 2009 #4
    Oh, that makes sense
     
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