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Exercise 8.2. Let a e Sym (10) be given by α= = (1357) (126) (379) (0543) Write a as a product of disjoint cycles.

Exercise 8.2. Let a e Sym (10) be given by α= = (1357) (126) (379) (0543) Write a as a product of disjoint cycles.

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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[sets and number] please explain it using simple words and step by step, thanks :)

Exercise 8.2. Let a e Sym(10) be given by a = (1357) (126) (379)(0543) Write a as a product of disjoint cycles.
Transcribed Image Text:Exercise 8.2. Let a e Sym(10) be given by a = (1357) (126) (379)(0543) Write a as a product of disjoint cycles.
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soyry, I think u might get wrong. Because u start from left to right in this part, u can check it on my image. Actually, the composition of transpositions should start from right to left. 

→ = (1357) (126) (379) (0543) @ Sym (10). 8 2 S L Step 2: Write as product of disjoint cycles We have Now, write all cycle as permutation, weget 2 = 0 I 2 อ 1 0 1 2 3 4 5 6 7 8 9 03 25 4 7 6 1 89 (st x = (13 (135)) (136) (37-19) (0 543) e Syndin). x = ( 3 4 5 6 7 8 9 7 4 5 6 9 83 Now multiply all permutations, 2 3 4 439 0 2 6 3 4 1 512 DO 12= poros=4 = $(8 (814))) So we need to start from 4 So 07 1-2 2→6 31 2 3 4 5 6 7 8 9 1789 2 3 4 5 6 7 8 97 0 3 4678 get we 8 128 (9) rather than 1.
Transcribed Image Text:→ = (1357) (126) (379) (0543) @ Sym (10). 8 2 S L Step 2: Write as product of disjoint cycles We have Now, write all cycle as permutation, weget 2 = 0 I 2 อ 1 0 1 2 3 4 5 6 7 8 9 03 25 4 7 6 1 89 (st x = (13 (135)) (136) (37-19) (0 543) e Syndin). x = ( 3 4 5 6 7 8 9 7 4 5 6 9 83 Now multiply all permutations, 2 3 4 439 0 2 6 3 4 1 512 DO 12= poros=4 = $(8 (814))) So we need to start from 4 So 07 1-2 2→6 31 2 3 4 5 6 7 8 9 1789 2 3 4 5 6 7 8 97 0 3 4678 get we 8 128 (9) rather than 1.
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