4. Cosets and Lagrange’s Theorem

Index — Quiz

Test your understanding of index with 5 practice questions.

Practice Questions

Question 1

What is the index of a subgroup $H$ in a group $G$?

Question 2

If $|G|=24$ and $|H|=6$ for a subgroup $H\le G$, what is $[G:H]$?

Question 3

What is the index of $G$ in itself, $[G:G]$?

Question 4

In the group $\mathbb{Z}$, what is the index $[\mathbb{Z}:4\mathbb{Z}]$?

Question 5

How many left cosets does a subgroup of index $7$ have?