Subgroups of Chevalley groups over rings. (English) Zbl 1498.20125
J. Math. Sci., New York 252, No. 6, 829-840 (2021) and Zap. Nauchn. Semin. POMI 484, 121-137 (2019).
Summary: Let \(R\) be a commutative ring. The lattice of subgroups of a Chevalley group \(G ( \Phi,R)\) containing the subgroup \(D(R)\) is studied, where \(D\) is a subfunctor of \(G ( \Phi,\_)\). Assuming that over any field \(F\) the normalizer of the group \(D(F)\) is “closed to be maximal,” it is proved that under some technical conditions the lattice is standard. A condition, on the normalizer of \(D(R)\) is studied in the case, where \(D(R)\) is the elementary subgroup of another Chevalley group \(G ( \Psi,R)\) embedded into \(G ( \Phi ,R)\).
MSC:
| 20G35 | Linear algebraic groups over adèles and other rings and schemes |
| 20E07 | Subgroup theorems; subgroup growth |
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