(2,3)-generation of exceptional groups

被引:31
作者
Lübeck, F
Malle, G
机构
[1] Rhein Westfal TH Aachen, Lehrstuhl Math D, D-52062 Aachen, Germany
[2] Univ Kassel, Fachbereich Math Informat, Kassel, Germany
来源
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 1999年 / 59卷
关键词
D O I
10.1112/S002461079800670X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 E-7 and E-8 over fields of odd characteristic occur as Galois groups of geometric extensions of Q(ab)(t), where Q(ab) 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.
引用
收藏
页码:109 / 122
页数:14
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