Overgroups of subsystem subgroups in exceptional groups: inside a sandwich. (English. Russian original) Zbl 1522.20192
St. Petersbg. Math. J. 34, No. 4, 591-609 (2023); translation from Algebra Anal. 34, No. 4, 47-73 (2022).
Summary: This paper supplements a previous paper by the author [St. Petersbg. Math. J. 32, No. 6, 1011–1031 (2021; Zbl 07436571); translation from Algebra Anal. 32, No. 6, 72–100 (2021)], where the overgroup lattice of the elementary subsystem subgroup \(E(\Delta ,R)\) of the Chevalley group \(G(\Phi ,R)\) for a sufficiently large root subsystem \(\Delta\) was studied. Currently, the subject-matter is the relationship between the elementary subgroup \(\widehat{E}(\sigma )\) given by a net of ideals \(\sigma\) of the ring \(R\), and the stabilizer \(S(\sigma )\) of the corresponding Lie subalgebra of the Chevalley algebra. In particular, it is proved that under a certain condition the subgroup \(\widehat{E}(\sigma )\) is normal in \(S(\sigma )\), and some properties of the corresponding quotient group are established.
MSC:
| 20G15 | Linear algebraic groups over arbitrary fields |
Keywords:
Chevalley groups; commutative rings; subsystem subgroups; normality of elementary subgroup; nilpotent structure of \(K_1\)Citations:
Zbl 07436571References:
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