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 ).

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1999-05-26