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Abstract
Quadratic groups, whose definitions depend on form parameters, contain the orthogonal groups, symplectic groups, classical unitary groups and all the classical groups of Dieudonné [Citation4] as well as those of Bruhat and Tits [Citation2]. Gauss decomposition with prescribed semisimple part in these groups is presented. As an application, the analog of a conjecture of Thompson is also studied for these groups.
ACKNOWLEDGMENTS
The authors are grateful to professor N. Gordeev for introducing them to this subject and for some helpful discussions. They are also grateful to E. W. Ellers and the referee for helpful comments and suggestions on a earlier version.
The article is supported in part by National Natural Science Foundation of China (10526016), and Science Research Foundation in Harbin Institute of Technology (HITC200701).
This work of the first two authors is supported partially by National Natural Science Foundation of China (10526016), National Natural Science Foundation of China (10571033), Development Program for Outstanding Young Teachers in Harbin Institute of Technology (HIT. 2006.54) and Science Research Foundation in Harbin Institute of Technology (HITC200701).
Notes
Communicated by A. Olshanskii.
Dedicated to Prof. Hong You on the occasion of his 60th birthday.