4. Cosets and Lagrange’s Theorem

Consequences Of Lagrange’s Theorem — Quiz

Test your understanding of consequences of lagrange’s theorem with 5 practice questions.

Practice Questions

Question 1

Let $G$ be a finite group with $|G|=12$. Which of the following must be the order of a subgroup of $G$?

Question 2

Let $G$ be a finite group with $|G|=15$. Which of the following cannot be the order of an element of $G$?

Question 3

If a finite group $G$ has prime order $7$, which statement must be true?

Question 4

If $|G|=20$ and $|H|=4$ for a subgroup $H$ of $G$, what is the index $[G:H]$?

Question 5

Which statement is a consequence of Lagrange’s theorem for a group whose order is prime?