Compute the fixed point sets X9 and the stabilizers G for each of the following permutation...

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Compute the fixed point sets X9 and the stabilizers G₂ for each of the following permutation groups G acting on the set X. (a) X = {1,2,3} and G = S3 = {(1), (12), (13), (23), (123), (132)} (b) X = {1, 2, 3, 4, 5, 6} and G = {(1), (12), (345), (354), (12) (345), (12)(354)} Compute the fixed point sets X9 and the stabilizers G₂ for each of the following permutation groups G acting on the set X. (a) X = {1,2,3} and G = S3 = {(1), (12), (13), (23), (123), (132)} (b) X = {1, 2, 3, 4, 5, 6} and G = {(1), (12), (345), (354), (12) (345), (12)(354)}

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