Let G be a finite group and let sym(G) be the group of all permutations on G. For each g in G, let g denote the element of sym(G) defined by g(x)gag action g . Give an example in which the mapping g...

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Extracted text: Let G be a finite group and let sym(G) be the group of all permutations on G. For each g in G, let g denote the element of sym(G) defined by g(x)gag action g . Give an example in which the mapping g ¢g is not 1 gxg for all x in G. Show that G acts on itself under the one-to-one.