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Unformatted text preview: 2 S 4 . (a) = (b) = (c) = id 7. Factor each of the following permutations into disjoint cycles. Using your answer express the inverse as a product of disjoint cycles. (a) 1 2 3 4 5 6 7 8 9 4 7 9 8 2 1 6 3 5 (b) 1 2 3 4 5 6 7 8 9 6 4 8 9 3 1 7 5 2 (c) 1 3 2 5 7 3 8 5 (d) 3 5 7 2 3 4 7 6 3 5 7 1 8. (a) How many permutations in S 5 x 1? (b) How many permutations in S 5 x both 1 and 3? 9. Let G = S 4 be the group of permutations of the set f 1 ; 2 ; 3 ; 4 g . For the purposes of this exercise it will probably be most convenient to write all elements of G in the disjoint cycle format. (a) Give a list of all of the distinct cyclic subgroups of G of order 4. (b) Given an example of a subgroup H of G of order 4 that is not cyclic. Math 4023 1...
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 Fall '09

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