Overgroups of exterior powers of an elementary group. Levels

Abstract

We prove a first part of the standard description of groups H lying between an exterior power of an elementary group Î m En(R) and a general linear group GL ( n m ) (R) for a commutative ring R, 2 ¾ R £ and n 3m. The description uses the classical notion of a level: for every group H we find a unique ideal A of the ground ring R which describes H.