Let G be a finite group and let sym(G) be the group of all
Chapter 29, Problem 13E(choose chapter or problem)
Problem 13E
Let G be a finite group and let sym(G) be the group of all permutations on G. For each g in G, let Φg denote the element of sym(G) defined by Φg(x) = gxg–1 for all x in G. Show that G acts on itself under the action g → Φg. Give an example in which the mapping g → Φg is not one-to-one.
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