Composition of Permutations

One of the reasons why the symmetric group Sym(n) is so interesting to group theorists is that it is relatively easy to understand, but non-abelian. This applet allows students to experiment with composing two permutations in Sym(4) to explore the properties of this group.

Students select two permutations, one from each drop-box. The composition of these permutations is shown both in cycle notation and by following the arrows from the left side all the way to the right.

Using the applet, the students can explore many concepts:

This page was created by James Hamblin, Associate Professor of Mathematics at Shippensburg University.