The class equation for a group G can be written |G| = |Z(G)| + E|CI(a;), where thesum runs over representatives of the distinct non-central conjugacy classes.Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}.Therefore the class equation of S3 is given by | S3| =1+2 +3.b)Explain why each of the following could not be the class equation of a group G.i)|G| = 3 + 3 + 3ii)|G| = 2 + 3 + 3 + 7iii)|G| = 1 + 3 + 6 + 8

Answered: Image /qna-images/answer/997aeeb9-ee85-44fa-bf92-3f3c508e5faa.jpg

Answered: Explain why each of the following could…

Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3 ii) |G| = 2 + 3 + 3 +7 iii) |G| = 1 +3 + 6 + 8

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

See similar textbooks

Related questions

Q: 3. Find the Taylor series expansion for the following function. f(x) = around 2 x+1

A: We know that the Taylor series is represented as:-∑n=0n=∞fnan!x-an=f(a)+f'(a)1!(x-a)+f''(a)2!(x-a)2+...

Q: S (a? - y)"y dy

Q: You owe your best friend $2,000. Because you are short on cash, you offer to repay the loan over 12 ...

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 52n 3 16 ac? c- B' n-3 Türkçe...

A: Introduction: When we add the terms of an infinite sequence, it becomes an infinite series. Likewise...

Q: Twenty-three slips of paper are each marked with a different letter of the alphabet and placed in a ...

Q: For items 46-50. Using a truth table, determine if the compound proposition -(rAs) +(¬sV¬r) is a tau...

Q: n What is the efficacy class of +- ? C: O (n) (4). A: O(1) B: O (log n) D: O (n log n) E: © (n')

Q: Let S be a set of linearly dependent vectors in R". Select the best statement. A. The set S cannot s...

Q: Consider the functions f(x, y) = sin¬' (9 – 2.0² – y²) and g(x, y) = x² – 4y². 1 %3D a. Identify and...

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) for you. If youwa...

Q: The sum of the elements of the eigenvector corresponding to the lowest value eigenvalue of matrix (V...

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

Q: Solve the differential Egueations Zydx - (3xy*dx- xdy =0 When

Q: 55 elementary classes will be chosen to participate in a school activities survey. There are 2323 el...

Q: V Solve using method of undetermined coefficients y"- 4y'+ 3y = 20 cas x

Q: Note: F=9 K=6 9х — (F — 11) a. Find the solution by graphing. b. Check if the point (F-16, F+4) is ...

Q: I Find the differential equation of the family of plane curves described, Draw at least three member...

Q: V Sove using variaton of parameters or reduction of order (D²+1)y = tan3x

Q: 4. Obtain the Fourier series expansion of the periodic function defined by f(t) = t³ + 3t for (0 <t ...

A: If f (x) is defined in the interval (a, b), then the Fourier series expansion is f(x)=12a0+∑n=1∞anco...

Q: The newly crowned Miss Universe Beatriz Luigi Gomez plans to buy fruits. A mango costs ₱20 each whil...

Q: 1. Lets, f(x) = xt – 5x3 + 9x2 a) Find all critical points and infection points, if any. b) The inte...

A: a. the critical points are the points where the derivative is zero or undefined. The given function ...

Q: In a club with 20 members, how many ways can a slate of 3 officers consisting of president, vice-pre...

A: This question is related to permutation and combination. The solution is given below

Q: Let V= R3 and W= {x:x = a(1; 0; 2) + b(1; –1;3)}, where a and b can be any real numbers. Is W subspa...

Q: 4. A bipartite graph G with a bipartition (X, Y) is defined as follows: X = {a, b, c, d} Y = (u, v, ...

A: This is a problem of Graph Theory.

Q: Calculate the directional derivative of f(x, y) = y – 2xy? at the point (0, 1) in the direction v = ...

A: Solution

Q: f(x+2)-(3) . f'(3) = lim is 1. n-3 x-1 . f'(1) = lim f(4x+1)-(5) is 4. n-1 x-1 , f'(1) = lim f(3x2+6...

A: Ghj

Q: (x-3y+2) dx +(3x+ 9y-12) dy -o 3.

Q: Find the measure of angle e in the oblique triangle below. Round your answer to the nearest degree. ...

A: we have given the triangle . we name it ∆ABC we have to find the angle θ i.e. ∠CAB

Q: E. Solve tne differential Equotions ☺ Czxy + xln3x)dy + .(xtyJ dx =0 when x =3, y=2

Q: Find the number of distinguishable permutations of the letters in each word below. (a) bigger (b) Bi...

Q: 1 0 -8 1 -8 -8 1 0 0 6 -9 1 6 -9 -48 -9 -9 1 0 = I -48 1 [ 0 1 1 A E, A E, E, A E, E2 E¡ A E, E, E, ...

A: A=10-80016-9-48, E1A=10-86-9-48001, E2E1A=10-80-90001, E3E2E1A=1000-90001, E4E3E2E1A=100010001=I ...

Q: Find the three Sylow 2-subgroups of D12 using its subgroup lattice below.

A: Given: Using D12's subgroup lattice below, determine the three Sylow 2-subgroups.

Q: Consider the experiment of tossing a die. Let A be the event of obtaining an odd number. Let B the e...

Q: Find the general solution of the following homogenous linear equations: 3. (9D²– 6D + 1) y = 0

Q: Find the number of distinguishable permutations of the digits of the number 3488384?

A: Let x be the number of distinguishable permutations. The given number is 3488384 The above number is...

Q: 30 H. 260 38

Q: Exercise 3.13. Let f : AB be a one-to-one correspondence. By Exercise 3.12, f-1: B → A is also a one...

A: see the attached image below

Q: Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the ...

A: Given , volume of cone = 97 cubic inches We know Volume of cone = 1/3 pi r^2 h

Q: A die is rolled 6 times. Find the probability of rolling no more than 4 fours. .... The probability ...

Q: circles with center on the x-axiv Aind the differential equation of the family of plane wres deucrib...

Q: ily of plane curves described and sketch several representative members of the family. 1.Parabolas w...

Q: 1. Apply the Sieve Process from 200 to 300.

A: Asper the company rule, we are supposed to solve one problem from a set of multiple problems. Theref...

Q: x2-7x+6 2. Lets, f(x) = x-10 a) Find all critical points, if any. b) The classification of each crit...

A: Introduction: The differential calculus is applicable to find the extremum of a real valued function...

Q: Perform the following as indicated. Show complete solution Given the systems of linear equations bel...

Q: 2. (Eisenstein arithmetic): Express your answers in the form x + yw. 2+5w-1-7w = (2+3w)·(5-w) = %3D ...

Q: 1 a b Let A = 0 5 2 0 0 1 Determine the condition of a and b so that A is diagonalisable. Let a =2 a...

Q: Suppose that a family has 7 children. Also, suppose that the probability of having a girl (based on ...

Q: EUMINATE THE ARBITRARY CONSTANTS yF Xax t

A: The given problem is to eliminate the arbitrary constants from given equation, to obtain the differe...

Q: Evaluate the second derivative of Z F5.png sin (b Vr2) f(x) = acosh cx3 if a = 5.54, b = 3, and c = ...

A: Introduction: There are three approximation formula for determining the derivatives of a function at...

Q: Bijective A function is bijective if it is both 1-1 and onto. Prove that the function below is not b...

Q: Q7. Evaluate the following: (x+3)dx -5 -2

Question

The class equation for a group G can be written |G| = |Z(G)| + E|CI(a;), where the
sum runs over representatives of the distinct non-central conjugacy classes.
Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}.
Therefore the class equation of S3 is given by | S3| =1+2 +3.
b)
Explain why each of the following could not be the class equation of a group G.
i)
|G| = 3 + 3 + 3
ii)
|G| = 2 + 3 + 3 + 7
iii)
|G| = 1 + 3 + 6 + 8

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?
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.
5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19:
10. Suppose that and are subgroups of the abelian group such that . If is a subgroup of such that , prove that .
27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.
Exercises 8. Find an isomorphism from the group in Example of this section to the multiplicative group . Sec. 16. Prove that each of the following sets is a subgroup of , the general linear group of order over .
Prove part c of Theorem 3.4. Theorem 3.4: Properties of Group Elements Let G be a group with respect to a binary operation that is written as multiplication. The identity element e in G is unique. For each xG, the inverse x1 in G is unique. For each xG,(x1)1=x. Reverse order law: For any x and y in G, (xy)1=y1x1. Cancellation laws: If a,x, and y are in G, then either of the equations ax=ay or xa=ya implies that x=y.
Exercises 10. Find an isomorphism from the multiplicative group to the group with multiplication table in Figure . This group is known as the Klein four group. Figure Sec. 16. a. Prove that each of the following sets is a subgroup of , the general linear group of order over . Sec. 3. Let be the Klein four group with its multiplication table given in Figure . Figure Sec. 17. Show that a group of order either is cyclic or is isomorphic to the Klein four group . Sec. 16. Repeat Exercise with the quaternion group , the Klein four group , and defined by
34. Suppose that and are subgroups of the group . Prove that is a subgroup of .
Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?
Exercises 35. Prove that any two groups of order are isomorphic.
1.Prove part of Theorem . Theorem 3.4: Properties of Group Elements Let be a group with respect to a binary operation that is written as multiplication. The identity element in is unique. For each, the inverse in is unique. For each . Reverse order law: For any and in ,. Cancellation laws: If and are in , then either of the equations or implies that .