On the Overgroups of EO(2l,R)

Abstract

Let R be a commutative ring with 1, let 2 ∈ R*, and let l ≥ 3. We describe the subgroups of the general linear group GL(n,R) that contain the split elementary orthogonal group EO(2l,R). For every intermediate subgroup H, there exists a unique maximal ideal A ⊴ R such that E(2l,R,A) ≤ H and, moreover, H normalizes EO(2l,R)E(2l,R,A). In the case where R = K is a field, similar results were obtained earlier by Dye, King, Li Shangzhi, and Bashkirov. Bibliography: 31 titles.