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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an Abelian group.
💡 Hint: Recall the definition of commutativity.
Question 2
Easy
Give an example of an Abelian group.
💡 Hint: Think of the number line.
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 an Abelian group?
- A group where operations are non-commutative
- A group where operations are commutative
- A random set of numbers
💡 Hint: Remember the distinction between commutative and non-commutative.
Question 2
Is the group of integers under multiplication an Abelian group?
- True
- False
💡 Hint: Consider numbers like 0.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation