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Section 2.9 in "Topics in Algebra" by Herstein details a construction of $\{G, T\}$ for a group $G$ and some automorphism $T \in \mathcal{A}(G)$ (which is not an inner automorphism). One of the constraints is $x^{-1} g^i x = gT^i$. Shouldn't it be $x^{-1} g^i x = (gT)^i = g^i T$?

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