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Let f= (4 5 6) and g = (1984) (2 7 5) (3 6) be two permutations in S9. (a) Compute fogo f-¹, and write the result in cycle notation. Show your work. (b) You should see a similarity between the cycle notation for g and your answer to part (a). Precisely say what this similarity is in words, including explaining how f is involved. (c) On the basis of your answer to part (b), fill in the rest of this proposition in mathematical notation. Proposition. Let n be a positive integer and let f, g € Sn. Suppose that the cycle notation for g is (a1,1 a1,2 a1,k₁) (am, 1 am,2 am,km). Then the cycle notation for fogo f-¹ is

Let f= (4 5 6) and g = (1984) (2 7 5) (3 6) be two permutations in S9. (a) Compute fogo f-¹, and write the result in cycle notation. Show your work. (b) You should see a similarity between the cycle notation for g and your answer to part (a). Precisely say what this similarity is in words, including explaining how f is involved. (c) On the basis of your answer to part (b), fill in the rest of this proposition in mathematical notation. Proposition. Let n be a positive integer and let f, g € Sn. Suppose that the cycle notation for g is (a1,1 a1,2 a1,k₁) (am, 1 am,2 am,km). Then the cycle notation for fogo f-¹ is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f = (456) and g = (1984) (2 7 5) (36) be two permutations in S9. (a) Compute fogo f-¹, and write the result in cycle notation. Show your work. (b) You should see a similarity between the cycle notation for g and your answer to part (a). Precisely say what this similarity is in words, including explaining how f is involved. (c) On the basis of your answer to part (b), fill in the rest of this proposition in mathematical notation. Proposition. Let n be a positive integer and let f,g Sn. Suppose that the cycle notation for g is (a1,1 1,2 a₁, k₁)... (am, 1 am,2... am,km). Then the cycle notation for fogo f-¹ is
Transcribed Image Text:Let f = (456) and g = (1984) (2 7 5) (36) be two permutations in S9. (a) Compute fogo f-¹, and write the result in cycle notation. Show your work. (b) You should see a similarity between the cycle notation for g and your answer to part (a). Precisely say what this similarity is in words, including explaining how f is involved. (c) On the basis of your answer to part (b), fill in the rest of this proposition in mathematical notation. Proposition. Let n be a positive integer and let f,g Sn. Suppose that the cycle notation for g is (a1,1 1,2 a₁, k₁)... (am, 1 am,2... am,km). Then the cycle notation for fogo f-¹ is
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