Sn arithmetic drills

This page provides a quick way to practice two basic skills when working with the symmetric group. Please notify me if you encounter any errors or bugs.

Multiplication

Write the product in two-line notation.

∘

Write the product below (apply the right-hand permutation first):

Press Enter or Submit when ready.

Disjoint cycle decomposition

Write the permutation shown above in disjoint cycle notation. Separate the numbers in each cycle with commas; no symbol is required between cycles (you may omit the ∘ that the book includes in Section 8).

Use e for the identity permutation. Press Enter or Submit when ready.