Question: Let f: G H be a group homomorphism. If a G with (a) = n, and (f(a)) = k (in H), prove that

Let f: G → H be a group homomorphism. If a ∈ G with σ(a) = n, and σ(f(a)) = k (in H), prove that k|n.

Step by Step Solution

★★★★★

3.40 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If let n qk r 0 r k Then fa n fe ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

954-M-L-A-L-S (8558).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Sometimes we can infer something about tastes from observing only two choices under two different economic circumstances. A. Suppose we consume only beer and pizza (sold at prices p1 and p2...

Q:

Let f: G H be a group homomorphism onto H. If G is abelian, prove that H is abelian.

Q:

Let f: G H be a group homomorphism with eH the identity in H. Prove that (a) K = {x G|f(x) = eH] is a subgroup of G. (K is called the kernel of the homomorphism.) (b) if g G and x K, then gxg-1 ...

Q:

Let f: G H be a group homomorphism onto H. If G is a cyclic group, prove that H is also cyclic.

Q:

Let f : G H be a surjective homomorphism whose kernel is K. If S is a subgroup of H, then let S = { g G | f ( g ) S } . (a) Prove that S is a subgroup of G that contains K . (b) Let f denote the...

Q:

Prove either one (and only one) of the following two statements. Circle the letter for the statement you are proving. (a) Let o : G - H be a group homomorphism, and let /V be a normal subgroup of H....

Q:

Problem 2 Let o : G - H be a group homomorphism. Prove that Ker($) = {g E G| 6(g) = en} and Im() = {o(g)| g E G} are subgroups of G and H correspondingly

Q:

Let o: G - H be a group homomorphism. Let S' C G. Prove that o( (S) ) = (4(S))

Q:

3. (a) Is union of two subgroups again a subgroup? Justify your answer. (b) Let G be a group and let a be a fixed element of G. Show that C(a) {re G: ax = xa} is a subgroup of G. (c) Let f: G G be a...

Q:

Can you please help answer all of the questions. Thanks so much! :) 144 CHAPTER 3 DIFFERENTIATION 62. Compute the derivative of f(x) = x/ using the limit definition. 70. Match functions (A)-(C) with...

Q:

(Sandwich principles.) Let U be an open set in R n , and let a be a point of U. (a) Let f, g, h: U R be real-valued functions such that f(x) g(x) h(x) for all x in U. If f(a) = h(a)let's call the...

Q:

We have covered several ratios in this unit that users of financial statements can work with to evaluate a companys performance. However, not all ratios are important for or applicable to all...

Q:

Find examples of sets of companies that have chosen to (1) globalize and (2) not globalize the following functions: a. Manufacturing b. Procurement c. Maintenance d. Logistics e. Customer service f....

Q:

e. What is the difference between the budget and the exact cost? in 30 words What is the difference between the budget and the exact cost

Q:

1. Which of the following is a correct match? (a) McClellandERG theory (b) Skinnerreinforcement theory (c) Vroomequity theory (d) Lockeexpectancy theory 2. In Herzbergs two-factor theory, base pay is...

Q:

The partnership of Telliher, Bachra, and Lang has experienced operating losses for three consecutive years. The partners, who have shared profits and losses in the ratio of Thea Telliher, 60 percent,...

Q:

The inexperienced driver of an all-wheel-drive car applies too much throttle as he attempts to accelerate from rest up the slippery 10-percent incline. The result is wheel spin at all four tires,...

Q:

a. Convert the heading control for the UFSS vehicle shown on the back endpapers (Johnson, 1980) into a digitally controlled system. b. Find the closed-loop pulse transfer function, T(z), if T = 0.1...

Q:

Critics of grocery club cards give examples of card-member prices being equal to the regular product price at stores without customer loyalty programs. In other words, customers who want to get food...

Q:

When are the parties to an illegal agreement in pari delicto?

Q:

Set your graphing window to 0 ¤ x ¤ 24Ï and - 2 ¤ y ¤ 2. a. Graph equations in the form y = sinx/a + sin x/b, using the a- and b-values listed in the table. Record...

Q:

When a tuning fork for middle C is struck, the resulting sound wave has a frequency of 262 cycles per second. The equation y = sin (262 2x) is one possible model for this wave. a. Identify the...

Q:

Find all values of that satisfy each equation. Use domain 0

Q:

(-10.4 Points] DETAILS HARMATHAP12 1.3.055. Suppose that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions, can be modeled by N = 0.140x + 36.4 where is the number...

Q:

Let A be the part of a disk with radius 17 with the center of origin that lies in the second quadrant. The area of A is given by the following double integral in polar coordinates I92 1'20?) / f r,...

Q:

Go to a local library; collect a sample of books consisting of the ages of book (based on copyright dates). Plan and describe the sampling procedure, then use the results to construct a confidence...