Practice Corollary on Finite Groups - 15.2.3 | 15. Subgroups | Discrete Mathematics - Vol 3
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15.2.3 - Corollary on Finite Groups

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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 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

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is a subgroup?

  • A subset that meets certain criteria
  • Any subset of a group
  • A group with fewer elements

💡 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

Challenge Problems

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