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Counting principles

  1. Oct 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose that H is a subgroup of G such that whenever H a is not equal to H b.
    Then a H not equal to b H.
    Prove that g H g ^-H
    Contains H.
    For all g Is an element of G.



    2. Relevant equations


    3. The attempt at a solution
    I tried the contrapositive position
    ( sorry, I'm doing this on an iPhone and I can't access latex )
     
  2. jcsd
  3. Oct 14, 2016 #2

    fresh_42

    Staff: Mentor

    Are you sure you haven't a mistake in there? ##H \subseteq gHg^{-1}H## for all ##g\in G## means, ##H \trianglelefteq G## is a normal subgroup. What about ##G=Sym (3) = \{1,(12),(13),(23),(123),(132)\}## and ##H=\{1,(12)\}##?
     
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