4. Cosets and Lagrange’s Theorem

Left And Right Cosets — Quiz

Test your understanding of left and right cosets with 5 practice questions.

Practice Questions

Question 1

Which set is the left coset of $H$ determined by $a$ in a group $G$?

Question 2

Which set is the right coset of $H$ determined by $a$ in a group $G$?

Question 3

If $G$ is abelian, what is true about $aH$ and $Ha$ for any subgroup $H$ and any $a \in G$?

Question 4

In the additive group $\mathbb Z_8$, let $H = \{0,4\}$. What is the left coset $1+H$?

Question 5

If a subgroup $H$ has $6$ elements, how many elements does any left coset of $H$ have?