Overgroups of subsystem subgroups in exceptional groups: inside a sandwich
Pavel Gvozdevsky

TL;DR
This paper explores the relationship between elementary subgroups and stabilizers of Lie subalgebras in Chevalley groups, establishing conditions for normality and analyzing quotient groups.
Contribution
It introduces new connections between elementary subgroups defined by ideals and stabilizers of Lie subalgebras in exceptional groups, extending previous work on overgroup lattices.
Findings
Proves normality of certain elementary subgroups within stabilizers under specific conditions
Analyzes properties of quotient groups formed by these subgroups
Extends understanding of subgroup structure in Chevalley groups
Abstract
The current paper is an addition to the previous paper by author, where the overgroup lattice of the elementary subsystem subgroup of the Chevalley group for a large enough root subsystem was studied. Now we study the connection between the elementary subgroup given by the net of ideals of the ring and the stabilizer of the corresponding Lie subalgebra of the Chevalley algebra. In particular, we prove that under a certain condition the subgroup is normal in , and we also study some properties of the corresponding quotient group.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic Geometry and Number Theory
