Burnside's Lemma
| Description: This quiz is designed to test your understanding of Burnside's Lemma, a fundamental result in combinatorics that relates the number of orbits of a group action to the number of fixed points. | |
| Number of Questions: 15 | |
| Created by: Aliensbrain Bot | |
| Tags: combinatorics group theory burnside's lemma |
Let $G$ be a group acting on a set $X$. The number of orbits of $G$ on $X$ is equal to:
If a group $G$ acts on a set $X$ and every element of $X$ is fixed by every element of $G$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $H$ is a subgroup of $G$, then the number of orbits of $H$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is transitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is regular on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is doubly transitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is triply transitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is $k$-transitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is primitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is imprimitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is sharply transitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is semiregular on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is quasiprimitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is doubly quasiprimitive on $X$, then the number of orbits of $G$ on $X$ is:
Let $G$ be a group acting on a set $X$. If $G$ is triply quasiprimitive on $X$, then the number of orbits of $G$ on $X$ is: