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Please help with Algebra problem

  1. Dec 7, 2004 #1
    Calculate all the subgroups of D_4.
    Which of them are normal subgroups? (It can
    be shown that any subgroup containing half
    the elements of a group G is a normal
    subgroup, and if a has order 2 then {e,a} is
    a normal subgroup iff a commutes with all
    elements of G.)

    {e,R^2} happens to be a normal subgroup.
    Give the Cayley table of D_4/{e,R^2}.
     
  2. jcsd
  3. Dec 7, 2004 #2
    I have made out a Cayley Table for D4, but do not know how to calculate the subgroups. Please help!
     
  4. Dec 8, 2004 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    What the heck is R?

    Let D_4 be e,t,t^2,t^3,s,st,st^2,st^3 t the rotation s the reflection (see how explaining notation can help?)

    Let H be a proper subgroup. if H contains t, then it contains all its powers, and has order 4. It can contain no other elements as its order must divide 8, and hence would contain all elements.

    If H doesn't contain t then... do some thinking and use the definitions of things.
     
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