14.6 - Definition of Cyclic Group
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Practice Questions
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Define a cyclic group.
💡 Hint: What element can generate all the others?
Give an example of an infinite cyclic group.
💡 Hint: Think about numbers and addition.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a cyclic group?
💡 Hint: Think about how many elements are needed to generate a group.
True or False: Every finite group is cyclic.
💡 Hint: Consider groups like S_3.
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Challenge Problems
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Prove that the multiplicative group of integers modulo a prime is cyclic.
💡 Hint: Consider the structure of numbers under modulo operations.
Explain how to determine whether a given group is cyclic just by examining its elements and their orders.
💡 Hint: Use the group's order and test with generators.
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