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Math Help - Orders of elements for rotational symmetries of cube

  1. #1
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    Orders of elements for rotational symmetries of cube

    I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem.


    Here is the question:


    Suppose a cube is oriented before you so that from your point of view there is a top face, a bottom face, a front face, a back face, a left face, and a right face. In the group O of rotational symmetries of the cube, let x rotate the top face counterclockwise 90 degrees, and let y rotate the front face counterclockwise 90 degrees.


    (a) Find g in O such that gxg^{-1}=y and g has order 4.
    (b) Find h in O such that hxh^{-1}=y and h has order 3.
    (c) Find k in O such that kxk^{-1}=x^{-1}.


    Thanks in advance.
    Last edited by abscissa; November 2nd 2013 at 04:10 PM.
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