## Permutation Group

A finite Group of substitutions of elements for each other. For instance, the order 4 permutation group would rearrange the elements in the order . A Substitution Group of two elements is called a Transposition. Every Substitution Group with elements can be written as a product of transpositions. For example,

Conjugacy Classes of elements which are interchanged are called Cycles (in the above example, the Cycles are ).