14.4 - Order of a Group Element
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Practice Questions
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What is the identity element in a group?
💡 Hint: Think about the role of 0 in addition or 1 in multiplication.
Define the order of an element.
💡 Hint: What do you get when you finally reach the group's starting point?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the order of an element?
💡 Hint: Think about the cycle and repetition in operations.
In a cyclic group, can you have multiple generators?
💡 Hint: Consider the number of ways you can reach a full cycle.
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Challenge Problems
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Prove that if a group has an element with infinite order, it cannot be finite.
💡 Hint: Consider the implications of having a finite number of elements but extending indefinitely with one.
Given a group (Z/7Z, +), describe its properties and the order of each element.
💡 Hint: Think about how addition mod 7 would work, and apply the elementary properties.
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