Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-15T00:47:08.200Z Has data issue: false hasContentIssue false
  • English
  • Français

(2,3)-GENERATION OF EXCEPTIONAL GROUPS

Published online by Cambridge University Press:  01 February 1999

FRANK LÜBECK  and
GUNTER MALLE
FRANK LÜBECK
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, D 52062 Aachen, Germany. E-mail: Frank.Luebeck@math.rwth-aachen.de
GUNTER MALLE
Affiliation:
Fachbereich Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Straße 40, Germany. E-mail: malle@mathematik.uni-kassel.de.
Get access

Abstract

We study two aspects of generation of large exceptional groups of Lie type. First we show that any finite exceptional group of Lie rank at least four is (2,3)-generated, that is, a factor group of the modular group PSL2(ℤ). This completes the study of (2,3)-generation of groups of Lie type. Second, we complete the proof that groups of type E7 and E8 over fields of odd characteristic occur as Galois groups of geometric extensions of ℚab(t), where ℚab denotes the maximal Abelian extension field of ℚ. Finally, we show that all finite simple exceptional groups of Lie type have a pair of strongly orthogonal classes. The methods of proof in all three cases are very similar and require the Lusztig theory of characters of reductive groups over finite fields as well as the classification of finite simple groups.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 109 - 122
Copyright
The London Mathematical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)