7. Group Actions or Advanced Group Topics

Group Actions — Quiz

Test your understanding of group actions with 5 practice questions.

Practice Questions

Question 1

Which statement correctly describes a group action of $G$ on a set $X$?

Question 2

Let $\mathbb Z$ act on $\mathbb R$ by $n\cdot x=x+n$. What is $(-3)\cdot 5$?

Question 3

Under the natural action of $S_3$ on $\{1,2,3\}$ by permutation, what is the orbit of $1$?

Question 4

Under the natural action of $S_3$ on $\{1,2,3\}$, which set is the stabilizer of $1$?

Question 5

What does it mean for a group action on $X$ to be trivial?