27 (a) Show that (ki k2 ... kr) = (ki kr) (k1 kr-1). (ki k₂).
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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Question
Problem27
![-1
Ύ
26. Let y be any cycle of length r. If o E Sn, show that ayol is also a cycle of length r.
More precisely, if y = (k₁ k2 kr) show that oyo-¹ = (ok₁ ok₂
...
okr).
3),..., (1 n).
(c) Repeat (b) for the transpositions (1 2), (2 3),..., (n-1 n). [Hint: Use (a)
and Exercise 26.]
(d) If o= (1 2 3 n), show that each element of Sn is a product of the
permutations (12), o, and o-¹. [Hint: Use (b) and Exercise 26.]
28. Let o= (1 2 3
27 (a) Show that (ki k2
kr) = (k₁ kr) (ki kr-1) (ki k₂).
(b) Show that each o ES, is a product of the transpositions (12), (1
[Hint: Each transposition is such a product by (a) and Exercise 26.]
...
...
..
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Transcribed Image Text:-1
Ύ
26. Let y be any cycle of length r. If o E Sn, show that ayol is also a cycle of length r.
More precisely, if y = (k₁ k2 kr) show that oyo-¹ = (ok₁ ok₂
...
okr).
3),..., (1 n).
(c) Repeat (b) for the transpositions (1 2), (2 3),..., (n-1 n). [Hint: Use (a)
and Exercise 26.]
(d) If o= (1 2 3 n), show that each element of Sn is a product of the
permutations (12), o, and o-¹. [Hint: Use (b) and Exercise 26.]
28. Let o= (1 2 3
27 (a) Show that (ki k2
kr) = (k₁ kr) (ki kr-1) (ki k₂).
(b) Show that each o ES, is a product of the transpositions (12), (1
[Hint: Each transposition is such a product by (a) and Exercise 26.]
...
...
..
...
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