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Homework Help: Solvable groups

  1. Apr 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that a group of order 12p is solvable for any prime p greater than 11

    2. Relevant equations

    I'm not very good about solvability questions so if anybody has any good ideas I'd be interested to hear them.

    3. The attempt at a solution

    I know that that every group of order 12 is either isomorphic to A4 or has an element of order 6, but I'm not really sure how to use this.
  2. jcsd
  3. Apr 9, 2010 #2
    Call the group in question G. You know that G has a subgroup H of order p.

    If you can show that H is a normal subgroup of G, then you know that G is solvable if and only if H and G/H are solvable. It's considerably simpler to show that H and G/H are solvable (hint: H has prime order and G/H has order 12).
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