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Unformatted text preview: 20 1. ALGEBRAIC THEMES Remember that in multiplying permutations, the permutation on the right is taken first. The first of the permutations takes 1 to 4 and the second takes 4 to 7, so the product takes 1 to 7. The first leaves 7 fixed and the second takes 7 to 6, so the product takes 7 to 6. The first takes 6 to 5 and the second takes 5 to 4, so the product takes 6 to 4. The first takes 4 to 2 and the second leaves 2 fixed, so the product takes 4 to 2. The first takes 2 to 3 and the second takes 3 to 1, so the product takes 2 to 1. This “closes the cycle” .1 7 6 4 2/ . The first permutation takes 5 to 6 and the second takes 6 to 5, so the product fixes 5. The first takes 3 to 1 and the second takes 1 to 3, so the product fixes 3. Thus the product is 1 3 4 7 6 5 1 4 2 3 5 6 D 1 7 6 4 2 : Notice that the permutation D 1 4 2 3 5 6 is the product of the cycles 1 4 2 3 and 5 6 . Disjoint cycles commute; their product is independent of the order in which they are multiplied. For example,independent of the order in which they are multiplied....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Permutations

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