Question: Problem 9 Suppose G acts on the left on the set X via p : G x X - X. Let p : G -

Problem 9 Suppose G acts on the left on the set X via p : G x X - X. Let p : G - Sx be the corresponding permutation representation. Define the set of fixed points X of G in X as X" = {xEX| g . x = x Vg EG} CX. Prove that for any o E NSx (p(G) ) and any x E X we have o (x) EXG . (Here p(G) is the image of G inside Sx)

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