# Dickson group

From Encyclopedia of Mathematics

Revision as of 21:05, 15 November 2017 by Richard Pinch (talk | contribs) (see also Chevalley group)

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 [1]. 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 [2] (cf. Chevalley group). In particular, Chevalley's method makes it possible to obtain Dickson groups as well [3].

#### References

[1] | L.E. Dickson, "A new system of simple groups" Math. Ann. , 60 (1905) pp. 137–150 |

[2] | C. Chevalley, "Sur certains groupes simples" Tôhoku Math. J. , 7 (1955) pp. 14–66 |

[3] | R.W. Carter, "Simple groups of Lie type" , Wiley (Interscience) (1972) |

**How to Cite This Entry:**

Dickson group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dickson_group&oldid=42298

This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article