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Maximal subgroup of a group

  1. Dec 7, 2011 #1
    If G is a finite group and M is a maximal subgroup, H is a subgroup of G not contained in M. Then G=HM.

    Is this true?
  2. jcsd
  3. Dec 7, 2011 #2
    No. Can you find a counterexample?
  4. Dec 7, 2011 #3
    I tried, but I failed. Thanks.
  5. Dec 7, 2011 #4
    What could go wrong??
  6. Dec 7, 2011 #5
    S_{3}, <(12)> maximal, <(23)>, S_{3} not equal <(12)><(23)>
    Thank you very much.
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