Cayley's theorem
A finite group "G" of order "n" is linear of degree at most "n" over any field "K". This statement is sometimes called Cayley's theorem, and simply results from the fact that the action of "G" on the group ring "K"["G"] by left (or right) multiplication is linear and faithful. The finite groups of Lie type (classical groups over finite fields) are an important family of finite simple groups, as they take up most of the slots in the classification of finite simple groups.