Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (b) f 1 (c) fgf = f= Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1, 2), (3, 4, 5), ... ). Do not include 1-cycles (e.g. (2)) in your answer. (a) fg= = 9 = 1 2 3 4 5 6 7 24 6 5 1 3 7 1 3 2 3 4 5 6 1 2 7 5 6 4 Assume multiplication of permutations f.g obeys the rule (fg)(x) = f(g(x)) so (1, 3) (1, 2) = (1, 2, 3) not (1, 3,2).

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