Practice Characterization for Subgroups - 15.2.2 | 15. Subgroups | Discrete Mathematics - Vol 3
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

15.2.2 - Characterization for Subgroups

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a subgroup.

💡 Hint: Think about the interactions of a group with its subset.

Question 2

Easy

What is the closure property?

💡 Hint: What happens to elements when combined?

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

Which of the following must be true for a subset to be a subgroup?

  • It must be non-empty
  • It must contain the inverse of each element
  • It must fulfill closure property
  • All of the above

💡 Hint: Think about group properties.

Question 2

True or False: If a group is finite, every non-empty subset is a subgroup.

  • True
  • False

💡 Hint: Consider closure and inverse properties.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a group of symmetries of a square, determine a valid subgroup along with a proof using closure and inverses.

💡 Hint: Visualize the square and rotate it to see the outcomes.

Question 2

Design a finite group of order 30 and demonstrate Lagrange's theorem by detailing its subgroups.

💡 Hint: Use cyclical permutations to visualize group elements.

Challenge and get performance evaluation