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For <math>n \geq 3 </math> the symmetric group is non-abelian - that is, there exist <math>a,b</math> such that <math>a*b \neq b*a \ </math> in the symmetric group. <math>\mathbb{S}_1 \ </math> is the trivial group and <math>\mathbb{S}_2 \ </math> is isomorphic to <math>\mathbb{Z}_2 \ </math>.
For <math>n \geq 3 </math> the symmetric group is non-abelian - that is, there exist <math>a,b</math> such that <math>a*b \neq b*a \ </math> in the symmetric group. <math>\mathbb{S}_1 \ </math> is the trivial group and <math>\mathbb{S}_2 \ </math> is isomorphic to <math>\mathbb{Z}_2 \ </math>.
The order of <math>\mathbb{S}_n </math> is <math>n! </math>
== Unsolved Problem ==
== Unsolved Problem ==