I'm watching Harvard's abstract algebra course online and the professor says that the map f(g)(h)=ghg(adsbygoogle = window.adsbygoogle || []).push({}); ^{-1}is a homomorphism between the groups G and Aut(G). the thing that I don't understand is that whether ghg^{-1}is an element of Aut(G) or not. It must be an element of Aut(G) because It's in the image of f but I can't figure out how it is an element of Aut(G). Can someone clarify what f(g)(h) means at the first place? if h is the input, then what is f(g)? Is f(g)(h) the same thing as fog(h)? Shouldn't our input be from G and our output in Aut(G)? so if h is in G, Is ghg^{-1}an automorphism on the group G under its operation? I'm confused

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# Exhibiting a homomorphism f: G-> Aut(G)

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