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Math Help - Exam Prep Help

  1. #1
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    Exam Prep Help

    For the dihedral group(  D_4 \mbox{or} \ D_8 ) with  \sigma = \begin{pmatrix} 1&2&3&4\\2&3&4&1 \end{pmatrix} \ \mbox{and} \ \tau = \begin{pmatrix} 1&2&3&4\\2&1&4&3 \end{pmatrix} \mbox{and}  \ D_4 = { {1 , \sigma , \sigma ^{2}, \sigma ^{3}, \tau , \sigma \tau , \sigma ^{2} \tau , \sigma ^{3} \tau }}

    (3) Find  < \sigma^{2} , \tau > \ \mbox{and} \ <\sigma^{3} , \sigma \tau > ?

    (4) What are the left cosets of  <\tau>, <\sigma^{2}>, \mbox{and} \ <\sigma^{2}, \tau> ?

    (5) Prove if  <\tau> \ \mbox{and/or} \ <\sigma^{2}> is normal.

    (6) Construct the Cayley table of  g/<\tau>

    I've tried really hard to work these questions out. I worked out the first two questions (from the attached image above) but I'm having trouble with the four posted here. I really need to be shown how to do these otherwise I wont get it. Ive been working on these for about 6 hours and Im not getting anywhere.
    Last edited by Jhevon; April 29th 2009 at 08:49 PM.
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  2. #2
    Behold, the power of SARDINES!
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    This link may be helpful

    http://en.wikipedia.org/wiki/Examples_of_groups

    D_8 \mbox{ or } D_4 is the example you are looking for
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  3. #3
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    I've finished Q1's and 2 now, but I'm completely stuck on questions (3) - (6). My mid-term is tomorrow and I think I'll really need to know how to do this.
    Thanks to anyone who can help.
    Last edited by MrJack1990; April 30th 2009 at 06:05 PM.
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