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Math Help - Multiplication on the dihedral group.

  1. #1
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    Multiplication on the dihedral group.



    I'm very confused, because I've checked it a few times and I come up with the same answer. If s is even, j is positive. If s is odd, j is negative. Since n-j \neq j for every j, something must be wrong, right?

    Edit: After working on this problem for a while, I found that I am actually right, and whether or not s is even affects the multiplication. Now I'm stuck on another problem:

    Show that this is a group. I can't prove is associativity. Do I have to go through the case for the parity of each x? That's at least 16 separate cases!
    Last edited by davismj; June 3rd 2010 at 02:22 PM.
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