3. Permutation Groups

Cycle Notation — Quiz

Test your understanding of cycle notation with 5 practice questions.

Practice Questions

Question 1

What does the cycle $(1\,2\,3)$ mean as a permutation?

Question 2

Which cycle notation represents the permutation that swaps $1$ and $4$ and leaves $2$ and $3$ fixed?

Question 3

What is the inverse of the cycle $(1\,2\,4\,3)$?

Question 4

Using the usual right-to-left convention, what is the image of $1$ under $(1\,3)(2\,4)$?

Question 5

How many elements are moved by the cycle $(1\,2\,5)$?