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hw03 - Modern Algebra 1 Spring 2010 Homework 2.1 Due...

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Modern Algebra 1 Homework 2.1 Spring 2010 Due January 27 Exercise 1. Let σ = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 13 2 15 14 10 6 12 3 4 1 7 9 5 11 8 and let τ = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 14 9 10 2 12 6 5 11 15 3 8 7 4 1 13 . Find the cycle decompositions of each of the following permutations: σ , τ , στ , τσ , and τ 2 σ . Exercise 2. For each of the permutations α whose cycle decompositions you computed in the preceding exercise, determine the least n N so that α n = (1). Exercise 3.
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