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4) Find the smallest integer n such that an+3 = a. 5) Prove that a is an odd permutation. 6) Let ß = (7 3)(1 5 4). Determine aß-'a.

4) Find the smallest integer n such that an+3 = a. 5) Prove that a is an odd permutation. 6) Let ß = (7 3)(1 5 4). Determine aß-'a.

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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The image of 9 is 1 not 6 there is a mistake I need parts 4-5-6-7
Part B: Let S, be the symmetric group and let a be an element of S, defined by: 1 2 3 4 5 6 7 8 9 ). a = 5 4 3 2 9 8 6 7 6 1) Write a as a product of disjoint cycles. 2) Determine the order of a. 3) Calculate a2018 4) Find the smallest integer n such that an+3 = a. 5) Prove that a is an odd permutation. 6) Let ß = (7 3)(1 5 4). Determine aß-la. 7) Show that for any permutations a and ß in Sn, a*ß and ß have the same parity.
Transcribed Image Text:Part B: Let S, be the symmetric group and let a be an element of S, defined by: 1 2 3 4 5 6 7 8 9 ). a = 5 4 3 2 9 8 6 7 6 1) Write a as a product of disjoint cycles. 2) Determine the order of a. 3) Calculate a2018 4) Find the smallest integer n such that an+3 = a. 5) Prove that a is an odd permutation. 6) Let ß = (7 3)(1 5 4). Determine aß-la. 7) Show that for any permutations a and ß in Sn, a*ß and ß have the same parity.
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