Normality of the Elementary Subgroups of Twisted Chevalley Groups over Commutative Rings

Abstract

In [6], G. Taddei has studied normality of the elementary subgroups of Chevalley groups over commutative rings. In this paper, applying the same method as used in his paper, we study normality of the elementary subgroups of twisted Chevalley groups over commutative rings. The main theorem is stated in Section 1. In Section 2, we deal with some subgroups over quotient rings. Under a key proposition which is proved in Section 4, we prove the main theorem in Section 3. We shall freely use the definitions, the notations, and the relations between elements of twisted Chevalley groups over commutative rings given in E. Abe [2].