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Proof on Dihedral Groups

  1. Mar 16, 2009 #1
    Let n be a positive integer and let m be a factor of 2n. Show that Dn (the dihedral group) contains a subgroup of order m.

    I'm not really sure where to start with this one. I know that Dn is generated by two types of rotations: flipping the n-gon over about an axis, and rotating it 2π/n around an axis through the center. But how do I show that you can have a subgroup of order m for every factor of 2n?

  2. jcsd
  3. Mar 17, 2009 #2

    matt grime

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    What if m divides n? What if m does not divide n? What is a polygon with m, or m/2 sides compared to one with n sides?
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