One of the first topics often taught in an abstract algebra class is
permutations, since they provide good examples of non-commutative finite
groups which the students can manipulate and visualize. This visualization
is often done through symmetry groups. For students who are less
geometrically inclined, however, the use of permutation ciphers provides
another good way of motivating permutations. They can easily be used to
illustrate composition, non-commutativity, inverses, and the order of group
elements, which are fundamental topics in group theory. We will give
examples of how this can be done and suggest other courses besides abstract
algebra in which this could also prove useful.