So I know this is the orbit-stabilizer theorem. I saw it in Hungerford's Algebra (but without that name). So we want to form a bijection between the right cosets of the stabilizers and the orbit. Could I define the bijection as this: f: gG/Gx--->gx Where H=G/Gx f(hx)=gx h in H ^ Is that what the function is suppose to look like? I'm really stuck on understanding the proof since it doesn't show me this function but it guarantees that it is a bijection. I'm not sure if there is a better way to word this question except, perhaps, what is the function between the right cosets and the orbit.