5. Normal Subgroups and Quotient Groups

Canonical Examples — Quiz

Test your understanding of canonical examples with 5 practice questions.

Practice Questions

Question 1

For any group homomorphism $f:G\to H$, which subset of $G$ is always a normal subgroup?

Question 2

Which statement is true for every abelian group $G$?

Question 3

Which subgroup of $S_n$ is the set of even permutations?

Question 4

In the quotient group $G/N$, what is the identity element?

Question 5

Which quotient group is isomorphic to $\mathbb Z/3\mathbb Z$?