Exercise 3.1. Let G be a group. Given g € G, define ig : G → G by ig(x)=gxg, Vx Є G. (1) Show that i, is an isomorphism of G with itself (i.e. an automorphism of G). (2) Show that CG(g) = {x G | ig(x) = x} = {x = G | xg = gx} is a subgroup of G, called the centralizer of g in G.

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