TY - JOUR

T1 - Subgroups of Chevalley Groups Over Rings

AU - Lubkov, R.

AU - Stepanov, A.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85099456479&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05203-x

DO - 10.1007/s10958-021-05203-x

M3 - Article

AN - SCOPUS:85099456479

VL - 252

SP - 829

EP - 840

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -