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Math Help - a certain group as 12 elements

  1. #1
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    a certain group as 12 elements

    A certain group has twelve elements:
    e, ρ, ρ^2, ρ^3, ρ^4, ρ^5
    R, ρR, ρ^2R, ρ^3R, ρ^4R, ρ^5R.

    They satisfy the three equations:
    ρ6= e, R^2= e, Rρ = ρ^5R.

    Using just the equations above, show that Rρ^3= ρ^3R.
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  2. #2
    Master Of Puppets
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    Re: a certain group as 12 elements

    I can see that R^2 = \rho^6 \implies R^2 = (\rho^3)^2 \implies R=\rho^3
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