Finitely Generated Abelian Groups: Classification & Examples

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 NOT always true about finitely generated abelian groups?

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1. Which of the following is NOT an example of a generating set for the group of integers together with addition?

2. How many different finitely generated abelian groups of size 2 are there?

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About This Quiz and Worksheet

With the use of this combination of a quiz and worksheet, you can find out what you know about finite abelian groups. Questions ask you about examples of a generating set for a group of integers, as well as what must be isomorphic to one of the groups in order 8.

Quiz and Worksheet Goals

To find out how much you understand about the lesson, the quiz questions ask about the following subjects:

  • Characteristics of finitely generated abelian groups
  • The number of groups of size 2
  • How many groups of order 4 exist
  • What has to be isomorphic to one of the groups of order 8

Skills Practiced

  • Knowledge application - use what you know to answer questions about groups of order 4
  • Information recall - remember what you have learned about groups of size 2
  • Defining key concepts - ensure that you can name some characteristics of finitely generated abelian groups

Additional Learning

To find more about the material, click on the lesson titled Finitely Generated Abelian Groups: Classification & Examples. By accessing the lesson, you can explore the additional subjects in the bullet list below:

  • The fundamental theorem of finitely generated abelian groups
  • Cyclic groups
  • Examples of groups
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