Group Homomorphisms: Definitions & Sample Calculations


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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, +)?

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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?

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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