Practice Abelian Groups (13.6.1) - Group Theory - Discrete Mathematics

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define an Abelian group.
Show hintHide hint
Recall the definition of commutativity.
Question 2.
Give an example of an Abelian group.
Show hintHide hint
Think of the number line.
3Question 3.
What is an Abelian group?
- A group where operations are non-commutative
- A group where operations are commutative
- A random set of numbers
Show hintHide hint
Remember the distinction between commutative and non-commutative.
4Question 4.
Is the group of integers under multiplication an Abelian group?
- True
- False
Show hintHide hint
Consider numbers like 0.
Question 5.
Show that for any Abelian group (G, *), if a, b, and c belong to G, then a * (b * c) = (a * b) * c.
Show hintHide hint
Start by applying the definition of associativity.
Question 6.
Given two Abelian groups, G1 and G2, prove that their direct product G1 x G2 is also an Abelian group.
Show hintHide hint
Check how operations interact in the composite set.

4 more questions in this section. Enroll free to practise them all.