Practice Definition of Subgroups - 15.2.1 | 15. Subgroups | Discrete Mathematics - Vol 3
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15.2.1 - Definition of Subgroups

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Learning

Practice Questions

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

Interactive Quizzes

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?

  • Contains the identity
  • Closure under operation
  • All of the above

💡 Hint: Think of the subgroup conditions we discussed.

Question 2

True or False: A subgroup can be empty.

  • True
  • False

💡 Hint: Remember the definition of a group.

Solve and get performance evaluation

Challenge Problems

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