13.6.1 - Abelian Groups
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
Define an Abelian group.
💡 Hint: Recall the definition of commutativity.
Give an example of an Abelian group.
💡 Hint: Think of the number line.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is an Abelian group?
💡 Hint: Remember the distinction between commutative and non-commutative.
Is the group of integers under multiplication an Abelian group?
💡 Hint: Consider numbers like 0.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Show that for any Abelian group (G, *), if a, b, and c belong to G, then a * (b * c) = (a * b) * c.
💡 Hint: Start by applying the definition of associativity.
Given two Abelian groups, G1 and G2, prove that their direct product G1 x G2 is also an Abelian group.
💡 Hint: Check how operations interact in the composite set.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.