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Homework Help: Subgroup proof - is this even true?

  1. Sep 9, 2014 #1
    1. The problem statement, all variables and given/known data

    Prove that G cannot have a subgroup H with |H| = n - 1, where n = |G| > 2.

    2. Relevant equations

    3. The attempt at a solution

    Counter-example, the multiplicative group R and its subgroup, multiplicative group R+. Or, the additive group Z, and its subgroup of integer multiples of 2. What am I missing here? I think this is trivial for finite groups, but they don't say finite groups, they don't say anything.
  2. jcsd
  3. Sep 9, 2014 #2


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    Saying n=|G| implies that the group is finite and has order n. Otherwise |H| = n - 1 wouldn't make much sense.
  4. Sep 9, 2014 #3

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