Overgroups of classical groups over commutative rings in linear group. (English) Zbl 1126.20033
For any commutative ring \(R\) with involution and 1, unitary groups \(\text{U}_{2n}R\subset\text{GL}_{2n}R\) (including symplectic, ordinary orthogonal, and standard unitary groups) are considered. All overgroups of \(\text{U}_{2n}R \) are described when \(n\geq 5\). The classification of normal subgroups of \(\text{U}_{2n}R,\) obtained previously by You-Vaserstein, is used.
Reviewer: L. N. Vaserstein (University Park)
MSC:
| 20H25 | Other matrix groups over rings |
| 20E07 | Subgroup theorems; subgroup growth |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
Citations:
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