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Question: let g be a group and let o g times...

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1. Let G be a group and let o: G xG G, (a, b) aba be the action of G On G by conjugation. Define Z(G) {a EGIab boa for all b EG) (a) Show that Z(G) Fix (G). (b) Suppose G is a p group with IGI> 1. Show that IZ(G)l 1. (Hint: Use (a) and the Fixed Point Formula)

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