Suppose that G acts on the set X. Prove that if g [tex]\in[/tex] G, x [tex]\in[/tex] X then Stab(adsbygoogle = window.adsbygoogle || []).push({}); _{G}(g(x)) = g Stab_{G}(x) g^{-1}.

Note: g Stab_{G}(x) g^{-1}by definition is {ghg^{-1}: h [tex]\in[/tex] Stab_{G}(x)}

My attempt at the problem is:

Let a [tex]\in[/tex] Stab_{G}(g(x)), then a(g(x)) = g(x) by definition.

Also Let b[tex]\in[/tex] Stab_{G}(x), then b(x) = x by definition.

and then I am completely stuck. Please guide me with this proof, I have tried for a couple hours.

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# Stabilizers (Group Theory)

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