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Do Isomorphic Groups Have Isomorphic Centers?
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[QUOTE="Mr Davis 97, post: 6050814, member: 515461"] I have one question that's slightly related to this one, and one which I don't want to create a new thread for. In trying to show that ##G \cong H \implies \operatorname{Aut} (G) \cong \operatorname{Aut} (H)##, one supposes that ##\phi : G \to H## and considers the map ##\theta:\text{Aut}(G)\rightarrow\text{Aut}(H)## defined as ##\theta(\psi)=\phi\circ\psi\circ\phi^{-1}## where ##\psi \in \operatorname{Aut} (G)##. One can then go to easily show that ##\theta## is an isomorphism. My question is, is there some reason why considering the map ##\theta## is the right thing to do? How would have I thought to consider that map? [/QUOTE]
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Do Isomorphic Groups Have Isomorphic Centers?
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