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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the identity element in a group?
💡 Hint: Think about the role of 0 in addition or 1 in multiplication.
Question 2
Easy
Define the order of an element.
💡 Hint: What do you get when you finally reach the group's starting point?
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 order of an element?
- The smallest positive integer for multiplication
- The highest exponent possible
- A measure of the group size
💡 Hint: Think about the cycle and repetition in operations.
Question 2
In a cyclic group, can you have multiple generators?
- True
- False
💡 Hint: Consider the number of ways you can reach a full cycle.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation