Overgroups of subsystem subgroups in exceptional groups: inside a sandwich

2021/07/02 by Pavel Gvozdevsky, Gvozdevsky, Pavel
Mathematics · #20G35(primary) 20G41 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2107.01249

openalex publication_date 2021/07/02 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

The current paper is an addition to the previous paper by author, where the overgroup lattice of the elementary subsystem subgroup E(Δ,R) of the Chevalley group G(Φ,R) for a large enough root subsystem Δ was studied. Now we study the connection between the elementary subgroup E(σ) given by the net of ideals of the ring R and the stabilizer S(σ) of the corresponding Lie subalgebra of the Chevalley algebra. In particular, we prove that under a certain condition the subgroup E(σ) is normal in S(σ), and we also study some properties of the corresponding quotient group.

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