So I know this is the orbit-stabilizer theorem. I saw it in Hungerford's Algebra (but without that name).(adsbygoogle = window.adsbygoogle || []).push({});

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/G_{x}--->^{g}x

Where H=G/G_{x}

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.

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# Bijection between Orbit and Stabilizer

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