Product of Permutations

The applet below serves a demonstration for the product of permutations. It displays two permutations, say f and g, of numbers 1, 2, ..., N in a circular arrangement and their product fg below. Recollect that, for 1 ≤ k ≤ N,

(fg)(k) = g(f(k)),

so that the left permutation is carried out first. (To emphasize this fact, (fg)(k) is often written as kfg.)

The elements of the two permutations are clickable: clicking on two elements in a sequence in either of the permutations multiplies that permutation by a transposition of the two elements.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?


  • Transpositions
  • Groups of Permutations
  • Sliders
  • Puzzles on graphs
  • Equation in Permutations

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