4 Let f = (4 5 6) and g = (1 9 8 4) (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 1,2 Then the cycle notation for fogo f-¹ is a₁,k₁)... (am,1 am,2 ...am,km).
4 Let f = (4 5 6) and g = (1 9 8 4) (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 1,2 Then the cycle notation for fogo f-¹ is a₁,k₁)... (am,1 am,2 ...am,km).
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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Transcribed Image Text:4 Let f = (4 5 6) and g = (1 9 8 4) (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 1,2
1
Then the cycle notation for fogo f-¹ is
·a₁, k₁) ・・・ (am,1 am,2 ···am,km).
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