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Homework Help: Subgroup of D_n

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    S.T <f> is not normal. where f is a reflection

    2. Relevant equations
    <f>={e,r^0 f, r^1f,r^2f,..}
    WTS For any g in D-n, g(r^kf)g^-1 Not In <F>

    3. The attempt at a solution
    Elements of D-n are r^k, r^kf
    For r^k, (r^k)(r^if)(r^-k) is in <f>.

    So I am stuck
  2. jcsd
  3. Apr 13, 2009 #2
    No. You want to show there exists such a g. Just find one.
  4. Apr 13, 2009 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    The subgroup generated by f, which is what <f> usually means, is just {e,f} with e the identity. What you wrote is in fact all of D_n. You probably should write in proper sentences so that everyone is sure what you mean (i.e. no abbreviations that might not be universally understood) - reading mathematics is hard at the best of times, so please help us out and make it as easy as possible.
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