6. Further Pure Mathematics

Group Theory — Quiz

Test your understanding of group theory with 5 practice questions.

Practice Questions

Question 1

In the alternating group $A_4$, how many elements of order 2 are there?

Question 2

What is the kernel of the sign homomorphism $\sgn\colon S_n\to\{1,-1\}$?

Question 3

Let $G$ be a group and define $H=\{g\in G\mid g^2=e\}$. Under which condition on $G$ is $H$ a subgroup of $G$?

Question 4

In the group $\mathbb{Z}_{15}$ under addition mod 15, what is the order of the element $[6]$?

Question 5

How many distinct subgroups does a cyclic group of order 30 have?