Unformatted text preview: Â´ 2 S 4 . (a) Â±Â´ = Â¿ (b) Â´Â¿ = Â± (c) Â´Â¿Â± = id 7. Factor each of the following permutations into disjoint cycles. Using your answer express the inverse as a product of disjoint cycles. (a) Â± 1 2 3 4 5 6 7 8 9 4 7 9 8 2 1 6 3 5 Â¶ (b) Â± 1 2 3 4 5 6 7 8 9 6 4 8 9 3 1 7 5 2 Â¶ (c) Â¡ 1 3 Â¢Â¡ 2 5 7 Â¢Â¡ 3 8 5 Â¢ (d) Â¡ 3 5 7 Â¢Â¡ 2 3 4 7 6 Â¢Â¡ 3 5 7 Â¢ Â¡ 1 8. (a) How many permutations in S 5 ï¬‚x 1? (b) How many permutations in S 5 ï¬‚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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