User Account

All Pages

Non-trivial homomorphism

Assignment Help Basic Statistics
Reference no: EM13965085

Let f:G->H be a group homomorphism.

Prove or disprove the following statement.

1.Let a be an element of G. If f(a) is of finite order, then a is also of finite order.

2.Let f be a surjection. Then f is an isomorphism iff the order of the element f(a) is equal to the order of the element a , for all a belong to G.

First, I want to know if f is the trivial homorphism, then both will fail, right?

Second, if f is non-trivial homomorphism. Both will hold, right?

Finally, Please help me to prove both or give me counterexamples without considering the trivial homomorphism.

Reference no: EM13965085

Questions Cloud

Explored the global business environment : We reviewed chapters two and three last night where we explored the global business environment.  We will focus on the global marketing environment in our upcoming class.  In preparation for this class, please read pages 106 - 165 in your textbook co..
You are a shareholder in a c corporation. this corporation : You are a shareholder in a "C" corporation. This corporation earns $5 per share before taxes. After it has paid taxes, it will distribute the remainder of its earnings to you as a dividend. The dividend is income to you, so you will then pay taxes on..
Better market their products and services to consumers : last week the company announces lower than expected net revenue and as a result, share prices dropped by 10% . the company's vice president of marketing would like your input on how the company can better market their products and services to consume..
Find a temperature at which they are the same length. : Find a temperature at which they are the same length. The coefficient of expansion of iron is 11 E -6 per C degree.
Non-trivial homomorphism : 2. Let f be a surjection. Then f is an isomorphism iff the order of the element f(a) is equal to the order of the element a , for all a belong to G. First, I want to know if f is the trivial homorphism, then both will fail, right? Second, if f is n..
What effect does temperature have upon surface tension : What effect does temperature have upon surface tension? Is it better to wash clothes in hot water or cold water?
What kind of relationship results are in this problem : Certain crystals fluoresce when exposed to a short burst of ultraviolet light. The amount of light emitted by the crystals is both time and temperature dependent. The emitted light is maximum at the time of excitation, the output then decaying wit..
Report for the mixing department for august : Prepare a cost reconciliation report for the Mixing Department for August.
What is the index of refraction of the gas : A Michelson interferometer has a vacuum chamber 5.0 cm long placed in one of its arms. The interferometer is illuminated with green laser light of wavelength lambda = 543.5nm. As an unknown gas is let into the vacuum chamber, 200 fringes are cou..

Reviews

Write a Review

Basic Statistics Questions & Answers

  Retail sales - neckwarmers

Neckwarmers. Mountainside Fleece sold 40 Neckwarmers. Solid-color neckwarmers sold for $9.90 each and print ones sold for $12.75 each.

  Employee turnover as the variables

How much of the variation in the dependent variable would be explained by the independent variable in this situation? Use job satisfaction and employee turnover as the variables for this problem.

  Type and assesses the amount of damage

A consumer group conducts crash test of new model cars. to determine the severity of damage to 2006 mazda 6s resulting from 10-mph crash into a concrete wall, the research group tests six cars of this type and assesses the amount of damage. descri..

  Provide a draft sexual harassment policy

Provide a draft sexual harassment policy that is in compliance with the latest Supreme Court decisions.

  Statistical correlations and regression analyses

Provide at least five real life examples where legislation and daily life choices have been driven by what could be defined basically as rooted in statistical correlations and regression analyses.

  Describe if the life expectancy of people in africa

A sociologist wants to describe if the life expectancy of people in Africa is lesser than the life expectancy of people in Asia.

  The length of the diffuser is 6 ft and the weight of the

a pipe diffuser consists of a diverging section of pipe . the diffuser is located in the horizontal plane. the diffuser

  Determine sample size to conduct a follow-up study

To conduct a follow-up study that would provide 95% confidence that the point estimate is correct to within plus-or-minus 0.04 of the population proportion, how large a sample size is required?

  Discuss the regression toward the mean phenomenon

When one of the five predictor variables in the preceding example is elimi- nated from the analysis, the value of R2 drops from 0.75 to 0.71. What does this tell us about the variable that was dropped?

  Explain use of the hypothesis testing

Explain how the use of the hypothesis testing can be used to evaluate solutions to the research issue.

  What is the population under consideration

What is the population under consideration

  Kinds of decision or actions are based on rankings

Nielsen publishes a weekly ranking of television programs as well as a weekly ranking of four major networks: ABC, CBS, NBC, and Fox. What kinds of decision or actions are based on the Nielsen rankings?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +1-415-670-9521

Phone: +1-415-670-9521

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd