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Normal subgroups of classical groups over von Neumann regular rings. (English) Zbl 0819.20052

Let \(R\) be a von Neumann regular ring. The pseudo-orthogonal groups \(O_{2n}R\) over \(R\), include the unitary, symplectic and ordinary orthogonal groups. The authors classify those subgroups of \(O_{2n}R\) which are normalized by the elementary orthogonal matrices, when \(n \geq 3\). The classification involves the notion of a form ideal of \(R\), introduced by Bass. The paper includes other results for the case \(n < 3\).

MSC:

20G35 Linear algebraic groups over adèles and other rings and schemes
20E15 Chains and lattices of subgroups, subnormal subgroups
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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