Vaserstein, L. N. Normal subgroups of orthogonal groups over commutative rings. (English) Zbl 0654.20052 Am. J. Math. 110, No. 5, 955-973 (1988). Let A be a commutative ring with identity, V a right A-module, and q a quadratic form on V. The aim of the present paper is to give a description of the normal subgroups of the orthogonal group O(q,A). To do this, the author introduces a subgroup E(q,A) and an overgroup G(q,A) of O(q,A), and, under reasonable mild assumptions on the quadratic form q, uses localization and patching to derive a complete description of all subgroups of G(q,A) which are normalized by E(q,A). This is the best result up to now. The result was announced by the author at the Sino-US Seminar on Classical Groups and Related Areas, Beijing, May, 18-23, 1987. Reviewer: Li Fuan Cited in 1 ReviewCited in 18 Documents MSC: 20G35 Linear algebraic groups over adèles and other rings and schemes 20E07 Subgroup theorems; subgroup growth 11E16 General binary quadratic forms 20H25 Other matrix groups over rings 20E15 Chains and lattices of subgroups, subnormal subgroups Keywords:quadratic form; normal subgroups; orthogonal group PDFBibTeX XMLCite \textit{L. N. Vaserstein}, Am. J. Math. 110, No. 5, 955--973 (1988; Zbl 0654.20052) Full Text: DOI