A classification of subgroups of \(\Lambda\)-quadratic groups normalized by relative elementary groups
In ``Subgroups of the general linear group normalized by relative elementary groups'' [Lect. Notes Math. 967, 1-22 (1982; Zbl 0536.20030)], \textit{A. Bak} proved the following sandwich theorem: Let \(A\) be a commutative ring satisfying Bass' stable range condition \(SR(M,A)\) and let \(m \geq \max (3,M)\). If \(H\) is a subgroup of \(GL_ m (A)\) normalized by some relative elementary subgroup, then \(H\) lies between a relative elementary subgroup and a slightly enlarged congruence subgroup. In the paper under consideration the author extends this result to subgroups of other classical groups. This is done in the framework of form-rings \((A, \Lambda)\) introduced by Bak [cf. \textit{A. Bak}, ``\(K\)- theory of forms'', Ann. Math. Stud. 98 (1981; Zbl 0465.10013)] under a suitable \(\Lambda\)-quadratic stable range condition.
\(\Lambda\)-quadratic stable range condition
scientific article; zbMATH DE number 745281