14.5 - Properties of Order of a Group Element
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Practice Questions
Test your understanding with targeted questions
Define the order of an element in a group. Give an example.
💡 Hint: Think about how many times you need to apply the operation to get back to the identity.
What is the identity element in a group?
💡 Hint: Consider the element that allows you to act without changing value.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the order of an element g in a group?
💡 Hint: Think about what it means for an element to return to the starting point.
True or False: An element with infinite order will eventually repeat itself.
💡 Hint: Consider the definition of infinite versus finite orders.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Prove that if in a finite cyclic group the orders of two distinct elements are equal, then those two elements must generate the same subgroup.
💡 Hint: Think about how many distinct elements can be produced by the powers of each element.
Demonstrate the necessity of the condition that the order of a generator must match the order of the cyclic group it generates.
💡 Hint: Reflect on what it means to cycle back through generated elements.
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