TY - JOUR

T1 - Subgroups of Chevalley groups over rings

AU - Lubkov, R.

AU - Stepanov, A.

PY - 2019/12

Y1 - 2019/12

N2 - In the present paper, we study the subgroup lattice of aChevalley group G(Φ, R) over a commutative ring R, containing thesubgroup D(R), where D is a subfunctor of G(Φ, ). Assuming thatover any field F the normalizer of the group D(F) is “closed to bemaximal”, we formulate some technical conditions, which imply thatthe lattice is standard. We also study the conditions concerning thenormalizer of D(R) in the case, where D(R) is the elementary subgroup of another Chevalley group G(Ψ, R) embedded into G(Φ, R)

AB - In the present paper, we study the subgroup lattice of aChevalley group G(Φ, R) over a commutative ring R, containing thesubgroup D(R), where D is a subfunctor of G(Φ, ). Assuming thatover any field F the normalizer of the group D(F) is “closed to bemaximal”, we formulate some technical conditions, which imply thatthe lattice is standard. We also study the conditions concerning thenormalizer of D(R) in the case, where D(R) is the elementary subgroup of another Chevalley group G(Ψ, R) embedded into G(Φ, R)

KW - Chevalley group

KW - subgroup lattice

KW - generic elemen

KW - universal localizatio

KW - normalize

KW - Transporter

M3 - Article

VL - 484

SP - 121

EP - 137

JO - ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН

JF - ЗАПИСКИ НАУЧНЫХ СЕМИНАРОВ САНКТ-ПЕТЕРБУРГСКОГО ОТДЕЛЕНИЯ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМ. В.А. СТЕКЛОВА РАН

SN - 0373-2703

ER -