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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the identity element.
💡 Hint: Think about what happens when something added to 0 or multiplied by 1.
Question 2
Easy
What does it mean for an element to be a generator?
💡 Hint: What structure would you use to generate other elements?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the identity element in group theory?
- An element that changes others
- An element that does not change others
- An element that has no inverse
💡 Hint: Think about what happens when combined with other elements.
Question 2
True or False: Every group can have more than one identity element.
- True
- False
💡 Hint: Consider the definition of identity.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation