Unformatted text preview: α and β for which ( αβ ) 2 6 = α 2 β 2 . 4. (Problem 2.32) If n ≥ 2, prove that the number of even permutations in S n is 1 2 n !. 5. (Problem 2.34) If n ≥ 3, show that if α ∈ S n commutes with every β ∈ S n , then α = (1). 6. Let α be the following permutation in S 9 ± 1 2 3 4 5 6 7 8 9 9 4 7 6 5 3 8 2 1 ² (a) Write α as a product of disjoint cycles. (b) Is α an even permutation or an odd permutation? Write it as a product of transpositions. (c) Find α1 , the inverse of α ....
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 Spring '11
 Johnson
 Algebra, Group Theory, following permutation, odd permutation

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