Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what makes a subgroup.
💡 Hint: Recall the group axioms.
Question 2
Easy
What is the closure property?
💡 Hint: Think of operations 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 the definition of a subgroup?
- A subgroup can only be empty
- A non-empty subset that is a group under the same operation
- Any subset of a group
💡 Hint: Consider the properties related to subsets.
Question 2
Can closure alone guarantee a subset is a subgroup in infinite groups?
- True
- False
💡 Hint: Think about the implications of it being infinite.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that every cyclic subgroup is abelian.
💡 Hint: Think of how elements generated by powers commute.
Question 2
Given the group of real numbers under addition, show that subsets like {x ∈ ℝ | x ≤ 0} and {x ∈ ℝ | x ≥ 0} are not subgroups.
💡 Hint: Can you find elements in the subsets that fail closure?
Challenge and get performance evaluation