Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
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.
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a subgroup in your own words.
💡 Hint: Think of it as a smaller group that still behaves like the big group.
Question 2
Easy
What are the properties needed for a subset to be a subgroup?
💡 Hint: There are three main points to remember.
Practice 4 more questions and get performance evaluation
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Is a non-empty subset of a group always a subgroup?
💡 Hint: Think about the defining properties of subgroups.
Question 2
What must be true for any two elements in a subgroup?
💡 Hint: Remember the definition of closure!
Solve and get performance evaluation
Push your limits with challenges.
Question 1
Given the group Z_12, identify all possible subgroups and their generators.
💡 Hint: Consider how elements combine under addition mod 12.
Question 2
Prove that every subgroup of a cyclic group is cyclic.
💡 Hint: Reflect on what it means for a generator to create elements of the group.
Challenge and get performance evaluation