symmetric group

Let X be a set. Let S(X) be the set of permutationsMathworldPlanetmath of X (i.e. the set of bijective functions on X). Then the act of taking the compositionMathworldPlanetmathPlanetmath of two permutations induces a group structureMathworldPlanetmath on S(X). We call this group the symmetric groupMathworldPlanetmathPlanetmath and it is often denoted Sym(X).

When X has a finite number n of elements, we often refer to the symmetric group as Sn, and describe the elements by using cycle notation.

Title symmetric group
Canonical name SymmetricGroup1
Date of creation 2013-03-22 14:03:53
Last modified on 2013-03-22 14:03:53
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 5
Author antizeus (11)
Entry type Definition
Classification msc 20B30
Related topic Symmetry2