4. Let S5 denote the symmetric group on the 5 letter set > let be elements of S5. -1 - (92234) 32104, 0 = Compute the following. (a) T (b) σοτ (C) τοσ (d) |S5 and {0, 1, 2, 3, 4), and (10342)

Q: 5. Let G be the multiplicative group {[2], [4], [6], [8]} = Z10-

A:

Q: An is the alternating group on n letters. What is |An|?

A:

Q: (a) Explain why it is impossible for any set of (real or complex) numbers which contains both 0 and…

A: To solve the given problem, we use the defination of group.

Q: 5. Find the number of generators of the cyclic group Z15

A: To find the number of generators of the cyclic group ℤ15.

Q: 2. Let G be a group. Pro-

A: Let G be a group .

Q: 4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2,…

A:

Q: (a) Make addition and multiplication tables for Z/3Z.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 1. Show that every group of prime order is simple.

A:

Q: 9. In a group, prove that (a"')"' - a

A:

Q: Find a matrix M such that M-¹0 (8) M = (19) for every element g € S3. Conclude that the…

A:

Q: 3. Solve the following Poisson equation problem by the finite difference method with h = k = 0.1.…

A: The Poisson equation is uxx+uyy=e-xyx2+y2. The conditions are ux, 0=1, ux, 1=e-x, u0, y=1, u1,…

Q: (6) Let (G, *) be a group and a € G. Prove that the order of a is equal to the order of a-1. Prove…

A:

Q: 7. Think about a mod 4 clock, with the numbers {0,1,2,3}. Is it a group for ?®? Can it be made into…

A:

Q: 1. Prove or disprove that each of the cises 52 of Section 3.1 is cyclic. a. Z2 × Z3

A: