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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a left coset in your own words.
💡 Hint: Consider which side the group element appears.
Question 2
Easy
What is the significance of Lagrange's theorem?
💡 Hint: Think about relationships between subgroups and their parent groups.
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 a left coset?
- A set of elements formed by subtracting a subgroup from a group
- A collection formed by multiplying a group element with a subgroup
- The same as a right coset
💡 Hint: Think about the multiplication order.
Question 2
True or False: The order of a subgroup divides the order of the group.
- True
- False
💡 Hint: Consider the implications of subgroup sizes.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a group of integers under addition modulo 8, identify the subgroup generated by 2. List the left cosets of this subgroup.
💡 Hint: Calculate by adding the group element to each member of the subgroup.
Question 2
In a group of order 12, if a subgroup has order 3, determine the number of distinct left cosets.
💡 Hint: Use Lagrange's theorem to divide the total group order by the order of the subgroup.
Challenge and get performance evaluation