14.3 - Group Exponentiation
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Practice Questions
Test your understanding with targeted questions
Define the identity element.
💡 Hint: Think about what happens when something added to 0 or multiplied by 1.
What does it mean for an element to be a generator?
💡 Hint: What structure would you use to generate other elements?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the identity element in group theory?
💡 Hint: Think about what happens when combined with other elements.
True or False: Every group can have more than one identity element.
💡 Hint: Consider the definition of identity.
1 more question available
Challenge Problems
Push your limits with advanced challenges
In a cyclic group of order 12, what is the order of the generator? Prove your reasoning.
💡 Hint: Consider how many unique group elements can be formed by repeated application of the generator.
For group G with elements g, g², g³ where g is a generator, determine if g⁴ can be expressed in terms of the existing elements.
💡 Hint: Check if g raised to a high exponent remains in the scope of the original elements.
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