The group of exponential automorphisms of a classical simple Lie algebra of type $G_2$ over a finite field $F$. If the order of $F$ is $q$, the order of the Dickson group is $q^6(q^2-1)(q^6-1)$. If $q>2$ the Dickson group is a simple group. These groups were discovered by L.E. Dickson . During the 50 years which followed no new finite simple group could be discovered, until a general method for obtaining simple groups as groups of automorphisms of simple Lie algebras was discovered by C. Chevalley  (cf. Chevalley group). In particular, Chevalley's method makes it possible to obtain Dickson groups as well .
|||L.E. Dickson, "A new system of simple groups" Math. Ann. , 60 (1905) pp. 137–150|
|||C. Chevalley, "Sur certains groupes simples" Tôhoku Math. J. , 7 (1955) pp. 14–66|
|||R.W. Carter, "Simple groups of Lie type" , Wiley (Interscience) (1972)|
Dickson group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dickson_group&oldid=42298