# Topics in Algebra, section 2.8. Definition of {G,T}

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 $$x^{-1} g^i x = (gT)^i = g^i T$$?