Group Homomorphisms: Definitions & Sample Calculations

Instructions:

Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

Which of the following is a correct explanation for why the function ƒ(x) = log(x) is a homomorphism from (R+, ·) to (R, +)?

Create Your Account To Take This Quiz

As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-free
Try it risk-free for 30 days. Cancel anytime
Already registered? Log in here for access

1. If today is Monday, what day of the week is 31 days from now?

2. Let ƒ(x) = |x|. Is ƒ a homomorphism from the integers under addition to the whole numbers under addition?

Create your account to access this entire worksheet
A Premium account gives you access to all lesson, practice exams, quizzes & worksheets
Access to all video lessons
Quizzes, practice exams & worksheets
Certificate of Completion
Access to instructors
Create an account to get started Create Account

About This Quiz & Worksheet

Our informative quiz and worksheet gives you a chance to gauge your comprehension level when it comes to group homomorphisms. When you answer these questions, you'll be asked about what makes a function a homomorphism, how to solve word problems involving homomorphisms and how to identify these functions when given examples.

Quiz & Worksheet Goals

This quiz asks you to perform the following objectives:

  • Explain why a function is a homomorphism
  • Solve word problems
  • Identify homomorphic functions from examples
  • Complete functions that are homomorphisms when given part of the function

Skills Practiced

  • Problem solving - use acquired knowledge to solve word practice problems
  • Reading comprehension - ensure that you draw the most important information from the related math lesson
  • Information recall - access the knowledge you've gained regarding why a function is a homomorphism
  • Knowledge application - use your knowledge to answer questions about how to complete homomorphisms

Additional Learning

If you'd like to learn more about this interesting topic, check out our lesson called Group Homomorphisms: Definitions & Sample Calculations. This lesson is designed to help you achieve the following goals:

  • Explain why understanding homomorphisms can be helpful
  • Detail the notation used to describe a group homomorphism
  • Define what preservation of operations means
Support