Practice Definition Of Cyclic Group (14.6) - Cyclic Groups - Discrete Mathematics

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6 sample questions

Question 1.
Define a cyclic group.
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What element can generate all the others?
Question 2.
Give an example of an infinite cyclic group.
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Think about numbers and addition.
3Question 3.
What is a cyclic group?
- A group generated by multiple elements
- A group generated by a single element
- A non-abelian group
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Think about how many elements are needed to generate a group.
4Question 4.
True or False: Every finite group is cyclic.
- True
- False
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Consider groups like S_3.
Question 5.
Prove that the multiplicative group of integers modulo a prime is cyclic.
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Consider the structure of numbers under modulo operations.
Question 6.
Explain how to determine whether a given group is cyclic just by examining its elements and their orders.
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Use the group's order and test with generators.

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