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Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a subgroup?
💡 Hint: Think about what group properties must hold.
Question 2
Easy
Define the closure property.
💡 Hint: Consider how operations behave in a group.
Practice 4 more questions and get performance evaluation
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a subgroup?
💡 Hint: Consider the definition of groups.
Question 2
True or False: Every subgroup has the same number of elements as its parent group.
💡 Hint: Think about examples with smaller subsets.
Solve 2 more questions and get performance evaluation
Push your limits with challenges.
Question 1
Given the set of real numbers, prove or disprove that the set of negative rational numbers is a subgroup under addition.
💡 Hint: Check closure when adding two elements from the subset.
Question 2
Consider a group of order 12 and a subgroup of order 3. How many distinct cosets can be formed from this subgroup?
💡 Hint: Utilize the relationship from Lagrange’s theorem.
Challenge and get performance evaluation