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Subgroups of Chevalley Groups Over Rings

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Let R be a commutative ring. The lattice of subgroups of a Chevalley group G(Φ,R) containing the subgroup D(R) is studied, where D is a subfunctor of G(Φ, — ).… Click to show full abstract

Let R be a commutative ring. The lattice of subgroups of a Chevalley group G(Φ,R) containing the subgroup D(R) is studied, where D is a subfunctor of G(Φ, — ). 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(Ψ,R) embedded into G(Φ,R).

Keywords: group; groups rings; subgroups chevalley; chevalley groups

Journal Title: Journal of Mathematical Sciences
Year Published: 2021

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