On the Stability of theK1-Functor for Chevalley Groups of Type E7

This paper is devoted to the study of the surjective stability of theK1-functor for Chevalley groups of type E7. This is a particular case of the stability problem for Chevalley groups, which was posed by H. Bass. In this paper, surjective stability of theK1-functor is proved under natural conditions on the dimension of the maximal spectrum of a ring and, independently, under a special condition which is meaningful from the point of view of equations defining a Chevalley group.