Answered: For a group G and a fixed element a ∈…

For a group G and a fixed element a ∈ G, define the subset C(a) to be the set of all elements in G that commute with a. C(a) = {g ∈ G : ag = ga} Let G = SL(2, R). Find C [1 1] [0 1]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 37E

See similar textbooks

Related questions

Q: Find as for the sequence defined by an 2ап-1 + 3, ао :1 (A) 11 (В) 29 (C) 61 (D) 17

Q: Using Newton-Raphson method, show that VN is given by Pn+1 N Pn + "dL){ =

Q: Let o : R → C be the map defined by p(x, y) = z, where z =x + iy. Let f: C -C be the function f(z) =...

Q: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x² cos(y...

Q: 5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago- nalizab...

Q: 2), the 2) = 30, ation an write t

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

Q: Now work on the following definitions of operation * on R. Indicate whether or not, a) It is commuta...

Q: Determine the definiteness of the quadratic form q(x) = xỉ + 2V6x,X2 + 2x3

Q: Let W be the set of all vectors of the form shown on the right, where b and c are arbitrary. Find ve...

Q: substitution y-erx in to given defind

A: We can solve by given information

Q: Let p : R → C be the map defined by p(x, y) = z, where z =x+ iy, Let f: C- c be the function f(z) = ...

Q: Co Ans.s.3sincis!20.

Q: 8. Without solving the following differential equations verify if the set of solutions is a vector s...

Q: Discretize the differential equation y"+y' +4ty= {t – )), y'(0) = 2, y'(3) = -2 with step-size h =

A: The differential equation given is as follows y''+y'+4ty=δt-32, y'0=2, y'3=-2 The central difference...

Q: 1. Prove that Si-2' = (n – 1) - 2"*+1 + 2 for any positive integer n.

Q: 4 — п 2n + 3) n=2

A: To find: the sequence is increasing, decreasing, monotonic, bounded below and bounded.

Q: of the following sets are subspaces of R? (1, Y, z) | 1 + y + z = 8} (-7, y, z) | y, z arbitrary num...

Q: Prove that 3" > n2 for every positive integer n.

Q: 1 -1 2 1 | -1 1 3 -1 1 Let, A = -1 3 -6 -2 1 4 3 -1 -5 1 a. Find a 5x5 matrix B such that AB = 0, wh...

A: Note :- You can cross check yourself to see that AB = 0.

Q: Part II: Recursion (10 pt.) 7. Give the first six terms (including the initial terms) of the followi...

Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled ...

A: Solution

Q: 25e230t sin² 40tt

Q: Let A be a matrix of Ma (K) B be a matrix of M, (K): C be a matrix of 8x2 Mixs Ck); D be a matrix of...

A: Here both expression doesnot exist which detailed solution given below

Q: 7. Armaan and Nazrat share a small cupcake making business. It takes Armaan 90 minutes to bake and d...

A: Let us first denote the work of baking and decorating the batch by 1 whole. In 90 minutes, Armaan d...

Q: Use appropriate Lagrange interpolating polynomial to approximate f(8.2) , if f(8.3) = 17.56,f(8.1) =...

A: The value of the table for x and y: x 8.3 8.1 8.6 y 17.56 16.94 18.51 We will approximate th...

Q: coso

A: Given csc θ=9 We shall find the value of cos θ

Q: Using the mathematical induction, verify that the following statement 1:(1!)+2·(2!)+.-+n-(n!) = (n+1...

Q: term

Q: 1 Find the general form of solution of the first order equation U + 2u, = (x – 2t)u + 2t2 + 3tx - 2x...

Q: Prove 1-3. 1. Show that the sum of two lower triangular matrices is a lower triangular.

A: We have to prove that the sum of two lower triangular matrix is a lower triangular.

Q: a differential equation that models the given situation. The stated rate of change is with respect t...

Q: F22) Determine one of the roots of f(x)=x' +1 · using the Newton Raphson method and an initial guess...

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to calculate the root of the equation: f...

Q: 7. Let z be a root of the polynomial p(z) = (z + 1)" + z". Show that %3D 1 Re z = - 2

A: For the solution follow the next step.

Q: Consider the following rational functions that have similar features. Which one doesn't belong with ...

A: Slant (Oblique) asymptotes: A rational function has a slant asymptote if and only if the degree of t...

Q: 2. Use the Newton-Raphson iteration method to estimate the root of the following function employing ...

Q: Which of the following statements is/are true regarding the matrix A? -51 0 2 3 A = | 1 -4 -9 7 A) T...

A: We have to find the correct statements for the given matrix A. For this, we have to find the rank of...

Q: The point P(x,x) moves on the curve y=x so that the x coordinate of P is increasing at a constant ra...

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

Q: Written assignment 1: Prove Proposition 6.39: Let n EN such that n> 1. Then n has a prime factorizat...

A: The problem is related to number theory. By strong induction assumption we try to prove proposition....

Q: x +x-5 Find lim 1-2x -x

Q: dy Find dr - 6.3% +1-6x (а) () (ii) Hence find the maximum height of the tunnel.

A: The height of the tunnel, in meters is y = -0.1 x3 +0.8 x2, 2≤x≤8

Q: Inv8 *Ve2x +1 dx 2. Find 2 In e Inv3

Q: The fox population in a certain region has an annual growth rate of 4 percent per year. It is estima...

Q: R.3. Suppose A C P(A). Prove that P(A) C P(P(A)).

A: Introduction: The power set of a set is very significant in the set theory. Every set has two trivia...

Q: Then, use this information to graph the function. (a) Choose the end behavior of the graph of f. Cho...

Q: 2) Parameterize the circle with radius 3, centered at the origin, running clockwise, which completes...

A: The parametric equations of a circle centered at origin are x(t) = rcos(kt), and y(t) = rsin(kt).

Q: If f(x) = log, (2x – 7) and g(1) = log, 3, find a value for x that satisfies f(x)= g(x). %3D

A: f(x) = g(x) => log4 (2x - 7) = log4 3 => 2x - 7 = 3

Q: (4) Decide if the following statements are true or false. If true, explain why. If false, give a cou...

A: (A) FALSE Consider the following series, ∑n=0∞anx-πn such that an = 1·3·5 . . . (2n-1)2·5·8 . . ....

Q: 1. Let X = {z €R:r#0,1} and define f : X X by f(r) = 1-. Prove or disprove that f is a permutation o...

A: As per our guidelines we are supposed to answer only first one. kindly reposed other part in the nex...

Question

For a group G and a fixed element a ∈ G, define the subset C(a) to be the set of all elements in
G that commute with a.

C(a) = {g ∈ G : ag = ga}

Let G = SL(2, R). Find C [1 1]
[0 1]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let be a subgroup of a group with . Prove that if and only if .
Let be a subgroup of a group with . Prove that if and only if
43. Suppose that is a nonempty subset of a group . Prove that is a subgroup of if and only if for all and .
Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .
Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.
5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19:
18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.
Prove that Ca=Ca1, where Ca is the centralizer of a in the group G.
15. Prove that if for all in the group , then is abelian.
Let be a group of order , where and are distinct prime integers. If has only one subgroup of order and only one subgroup of order , prove that is cyclic.
42. For an arbitrary set , the power set was defined in Section by , and addition in was defined by Prove that is a group with respect to this operation of addition. If has distinct elements, state the order of .
Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic group of order n. Prove that G has elements of order 12 but no element of order greater than 12. Find the number of distinct elements of G that have order 12.