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Permutation Group Proof

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose G is a group, H < G (H is a subgroup of G), and a is in G.

    Prove that a is in H iff <a> is a subset of H.

    2. Relevant equations
    <a> is the set generated by a (a,aa,aa^-1,etc)

    3. The attempt at a solution
    For some reason this seems too easy:

    1. Suppose a is in H.
    Since H is a group, a^-1 is in H.
    Since H is a group aa, is in H (as is aa^-1, etc.)
    Thus <a> is a subset of H.

    2. Suppose <a> is a subset of H.
    Obviously a is in H.

    And this completes the proof... or am I missing something?
  2. jcsd
  3. Oct 25, 2011 #2
    shameful bump
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