Geometriae Dedicata

, Volume 41, Issue 1, pp 63-87

First online:

Generation of exceptional groups of Lie-type

  • Thomas S. WeigelAffiliated withMathematisches Institut der Universität Freiburg

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In this paper we prove two theorems concerning the generation of a finite exceptional group of Lie-type G F. The first is: there is a semisimple element s such that for ‘nearly all’ elements xG Fthe elements s and x generate the group G F. The second theorem we prove is: if G is a finite simple exceptional group of Lie-type not of type E 6 or 2 E 6, then it is generated by three involutions.