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Group Theory Proof Help?

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Here's the question:

    2. Relevant equations

    3. The attempt at a solution

    Step 1: <S,T> subset <<S>,T> subset <<S>,<T>> (easy)
    and Step 2: <S,T> subset <S,<T>> subset <<S>,<T>> (easy)
    and Step 3: <<S>,<T>> subset <S,T> (slightly trickier)

    I've done step 1 and 2 by saying <S> is smallest subgroup of G containing all elements of S and similarly with T.

    No idea how to do step 3 i.e. how to show <<S>,<T>> subset <S,T> ??
  2. jcsd
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