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

If let n qk r 0 r k Then fa n fe ...

Let f: G H be a group homomorphism. If a G with (a) = n,

Question:

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.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 09:08 AM

See More Questions

Let f: G H be a group homomorphism onto H. If G is abelian, prove that H is abelian.
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 ...
Let f: G H be a group homomorphism onto H. If G is a cyclic group, prove that H is also cyclic.
Draw the BST that results when you insert the keys E A S Y QUE S T I O N in that order into an initially empty tree. What is the height of the resulting BST?
How does a complete performance management system differ from the use of annual performance appraisals?
The Electronic Controls Company (ECCO) is one of the largest makers of backup alarms in the world. Backup alarms are the safety devices that emit a high-pitched beeping sound when a truck, forklift,...
What is the best analysis path for breaking down a spectrum with a large number of peaks?
Suppose US$1 = 0.7809 in New York and US$1 = 0.7793 in Paris. How can foreign exchange traders profit from these exchange rates? What actions can they take that may result in the same dollar/euro...
Refer to the original data. Assume that the company sold 42,000 units last year. The sales manager is convinced that a 2% reduction in the selling price, combined with a $152,000 increase in...
Determine RTh and VTh at terminals 1-2 of each of the circuits of Fig. 4.101? (a) (b) 10 20 V 40 o 2 60 2 A 30
(a) Find all generators of the cyclic groups (Z12, +), (Z16, +), and (Z24, +). (b) Let G = (a) with (a) = n. Prove that ak, k Z+, generates G if and only if k and n are relatively prime. (c) If G is...
(a) Determine A2, A3, and A4. (b) Verify that {A, A2, A3, A4} is an abelian group under ordinary matrix multiplication. (c) Prove that the group in part (b) is isomorphic to the group shown in Table...
The following data were obtained for compounds of nitrogen and hydrogen: (a) Show that these data are consistent with the law of multiple proportions. (b) If the formula of compound B is N 2 H 2 what...
Mr. B died in 2019 at the age of 72. In his will, Mr. B made several bequests to the members of his family. The executor of Bs estate wants to know which of the following bequests constitute...
John Henry Harris was left a 1962 Impala convertible by his uncle, Billy Bob Harris. After receiving the car, John determined that five cars in his family were too many. As a result, he disclaimed...
An S corporation has an accumulated adjustments account balance of $50,000 at the beginning of the year and accumulated earnings and profits of $20,000. The corporation earns $40,000 for the year....
The $15,000 exclusion would be available in which of the following transfers? a. Revocable transfer in trust to W for life, then to S. b. Irrevocable transfer in trust to W for life, then to S. c....
Delta Corporation, a calendar-year S corporation, has an accumulated adjustments account of $8,000. It also has accumulated earnings and profits from pre-1983 years of $12,000. The sole shareholder...
For the following exercises, use the graphs to write the formula for a polynomial function of least degree. I 4-3 f(x) 1200 HE x
Review Exhibit 11.4. Analyze each product on the graph according to the characteristics that influence the rate of adoption. For example, what can you conclude from the data about the relative...
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...
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...
Find all values of that satisfy each equation. Use domain 0 < 360. a. tan = 0.5317 b. sec = - 3.8637 c. csc = 1.1126 d. cot = - 4.3315
The heights (in inches) for a sample of 22 male adults are 62, 82, 79, 76, 73, 70, 67, 64, 61, 80, 79, 75, 72, 69, 66, 63, 75, 75, 72, 72, 68, 68 Send data to calculator Draw the histogram for these...
What are the facts of this case? Business Financing Solutions, Inc. ("BFS") is a small lending institution that specializes in providing loans to small businesses. BFS's president, Rachel Chen, has...
Royal Lawncare Company produces and sells two packaged products-Weedban and Greengrow. Revenue and cost Information relating to the products follow: Selling price per unit Variable expenses per unit...

Let f: G H be a group homomorphism. If a G with (a) = n,

Question:

Step by Step Answer:

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

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions