14.7 - Examples of Cyclic Groups
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Practice Questions
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Define a cyclic group.
💡 Hint: Think about groups that can be fully defined by one number.
What is the identity element in a group?
💡 Hint: This element is critical for maintaining the structure of a group.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a cyclic group?
💡 Hint: Focus on the unique feature of cyclic groups.
True or False: The identity element is unique in any group.
💡 Hint: Consider the properties of identity in group theory.
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Challenge Problems
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Prove that the group of integers under addition is cyclic.
💡 Hint: Consider the operations performed by adding one repeatedly.
Show that every element of Z/7Z can be generated by an appropriate base, and identify the generators.
💡 Hint: Work modulo 7 and document each result.
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