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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- Dec 5th 2011, 11:34 AMsbacon1991a 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. - Dec 5th 2011, 12:03 PMpickslidesRe: a certain group as 12 elements
I can see that $\displaystyle R^2 = \rho^6 \implies R^2 = (\rho^3)^2 \implies R=\rho^3$