7. Group Actions or Advanced Group Topics

Orbits And Stabilizers — Quiz

Test your understanding of orbits and stabilizers with 5 practice questions.

Practice Questions

Question 1

For a group action of $G$ on a set $X$, what is the orbit of an element $x \in X$?

Question 2

For a group action of $G$ on a set $X$, what is the stabilizer of an element $x \in X$?

Question 3

If a finite group $G$ acts on a set $X$, which formula gives the orbit-stabilizer theorem for $x \in X$?

Question 4

If every element of $G$ fixes $x \in X$, what is $\operatorname{Stab}(x)$?

Question 5

Under the trivial action of $G$ on $X$, what is the orbit of any $x \in X$?