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 x is-an-element-of G(F) the 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 E6 or 2E6, then it is generated by three involutions
Weigel, T. (1992). Generation of exceptional groups of Lie-type. GEOMETRIAE DEDICATA, 41(1), 63-87 [10.1007/BF00181543].
Generation of exceptional groups of Lie-type
Weigel, TS
1992
Abstract
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 x is-an-element-of G(F) the 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 E6 or 2E6, then it is generated by three involutions
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