Hi

1)Given G, a group, and X a G-set What relationship exists between $\displaystyle G_x $ and $\displaystyle G_y $ if x and y belong to the same orbit?

2)

a)Let G be a group and X a G-set.Prove that there is a homomorphism

$\displaystyle p: G --------- Biy (X) $ determined by the action.

b)Now, given a homomorphism

$\displaystyle p: G ---------- Biy (X) $, show that X is a G-set

I hope some help. thanks