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Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a subgroup?
💡 Hint: Think about the definition of a group you learned before.
Question 2
Easy
List the three main properties a subset must satisfy to be a subgroup.
💡 Hint: Recall our classroom discussion on subgroup conditions.
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 property must a subset satisfy to be a subgroup?
💡 Hint: Think of the subgroup conditions we discussed.
Question 2
True or False: A subgroup can be empty.
💡 Hint: Remember the definition of a group.
Solve and get performance evaluation
Push your limits with challenges.
Question 1
Given a group G of order 15, list the possible orders of its subgroups. Prove your reasoning using Lagrange’s theorem.
💡 Hint: Find factors of 15.
Question 2
Construct a subgroup for the group of permutations on three objects. Show all properties hold.
💡 Hint: Consider how permutations combine and find pieces that remain closed.
Challenge and get performance evaluation