Why are certain transformations in the case of D4 group considered even or odd?

[LagrangeEuler]

Why $\rho,\rho^2,\rho^3,\rho^4$ are even transformation and $\rho\sigma,\rho^2\sigma,\rho^3\sigma$ are odd transformation. I'm talking about case of $D_4$ group, where $\rho$ is rotation and $\sigma$ is reflection.

 

[tiny-tim]

Hi LagrangeEuler!

What is the definition of even (or odd) transformation?

 

[LagrangeEuler]

Not sure.

 

[tiny-tim]

Not sure.

ok, if you can't give a "mathy" definition, just give an ordinary english explanation (or example), and we'll take it from there

(go back to your notes or your book, if necessary)

 

[HallsofIvy]

tiny-tim's point is, I expect, that you cannot expect to understand any explanation we give as to why a specific transformation is, or is not, even or odd if you do not know what the definition of "even" or "odd" transformation is. And in mathematics definition are "working" definitions- we use the precise words of definitions is proving things. So we would expect to use the precise words of the definitions of "even" and "odd" transformations in proving that certain transformations are even or odd.