Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Short description about dihedrals?

  1. Apr 13, 2007 #1
    Can someone give me a short description about dihedrals? for example what would be the elements of D10? or D4?
  2. jcsd
  3. Apr 13, 2007 #2
    Well, do you know the geometric interpretation of a dihedral group? The elements are (in the geometric interpretation) rotations and reflections.
  4. Apr 13, 2007 #3
    Yes I know the geometric interpretation. Is it the same for abstract algebra?
  5. Apr 13, 2007 #4
    Yes, the geometric interpretation is the motivation for dihedral groups. As I said, the elements are analogous to rotations and reflections. In general a group presentation for [itex]D_n[/itex] is

    [tex]\langle s, r| s^n = 1, r^2 = 1 \rangle.[/tex]

    In that presentation, s corresponds to a rotation and r to a particular reflection.
    Last edited: Apr 13, 2007
  6. Apr 13, 2007 #5


    User Avatar
    Science Advisor
    Homework Helper

    You also need [itex]sr = rs^{-1}[/itex] in that presentation.
  7. Apr 13, 2007 #6
    Indeed! I should be more careful. The group in my post isn't even finite for n>1. :yuck:
    Last edited: Apr 14, 2007
  8. Apr 14, 2007 #7

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    It is the free product of C_n and C_2, in fact.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook