5. Normal Subgroups and Quotient Groups

Factor Groups — Quiz

Test your understanding of factor groups with 5 practice questions.

Practice Questions

Question 1

If $N$ is a normal subgroup of $G$, which element acts as the identity in the factor group $G/N$?

Question 2

What is the factor group $\mathbb{Z}/4\mathbb{Z}$ isomorphic to?

Question 3

If $|G|=24$ and $|N|=6$, what is $|G/N|$?

Question 4

What condition must a subgroup $N$ satisfy for the set of cosets $G/N$ to form a group under $(aN)(bN)=abN$?

Question 5

In $G/N$, what is the inverse of the coset $gN$?