Exercise 2.What cycle is (a,a2 ... an)¯1?Exercise 3.Part A: Let G = Sn and let H = {a € G|a(1) = 1}. Show that H is a subgroup of G.Part B: Let S9 be the symmetric group and let a be an element of S9 defined by:1 2 3 4 5 6 7 8 95 4 3 29 8 67 6a =1) Write a as a product of disjoint cycles.2) Determine the order of a.3) Calculate a²2018.4) Find the smallest integer n such that a™+3 = a.5) Prove that a is an odd permutation.6) Let ß = (7 3)(1 5 4). Determine aß-'a.7) Show that for any permutations a and ß in Sn, a*ß and ß have the same parity. 12:37 A Mf Math365 Assign... /Exercise 4.Consider the following permutations in S9(12 3 4 5 6 7 8 9(1 2 3 4 5 6 7 8 9and r=(35 2 1 4 6 9 785 2 6 7 1 3 8 91) Write o,r, oand1' in cycle notation.2) Write o andas a product of 2-cycles.3) What is | o |? What is | 7|? And what is | ot |?4) Compute or .5) Find oro-, Write your answer in cycle notation.6) Find a by solving oa =r. Write your answer in cycle notation.2/2II...

Name: Exercise 2.What cycle is (a,a2 ... an)¯1?Exercise 3.Part A: Let G = S
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Description: Exercise 2.What cycle is (a,a2 ... an)¯1?Exercise 3.Part A: Let G = Sn and let H = {a € G|a(1) = 1}. Show that H is a subgroup of G.Part B: Let S9 be the symmetric group and let a be an element of S9 defined by:1 2 3 4 5 6 7 8 95 4 3 29 8 67 6a =1)

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Math

Advanced Math

Exercise 2. What cycle is (a,az ... an)~1?

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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