13 - Group Theory
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
What are the four axioms that define a group?
💡 Hint: Use the acronym C-A-I-I.
Give an example of a group under addition.
💡 Hint: Think about the properties of integers.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
Which property ensures that the result of an operation on two elements is still in the set?
💡 Hint: Think about how operations interact with set membership.
True or False: Every group operation must be commutative.
💡 Hint: Recall the definition of an Abelian group.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Prove that any finite subset of a group is also a group under the same binary operation, citing each of the group axioms.
💡 Hint: Focus on the properties of the larger group.
Given the set of integers modulo n, discuss how it forms a group with addition, relating it to all four axioms.
💡 Hint: Revisit properties of modulo arithmetic.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.