On the stability of the K-1-functor for Chevalley groups of type E-7

This paper is devoted to the study of the surjective stability of the K-1-f unctor for Chevalley groups of type E-7. This is a particular case of the s tability problem for Chevalley groups, which was posed by H. Bass. In this paper, surjective stability of the K-1-functor is proved under natural cond itions on the dimension of the maximal spectrum of a ring and, independentl y, under a special condition which is meaningful from the point of view of equations defining a Chevalley group. (C) 1998 Academic Press.