Geodesic
Subgroups of Chevalley groups over rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 484 (2019), pp. 121-137

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In the present paper, we study the subgroup lattice of a Chevalley group $\operatorname{G}(\Phi,R)$ over a commutative ring $R$, containing the subgroup $D(R)$, where $D$ is a subfunctor of $\operatorname{G}(\Phi,\_)$. Assuming that over any field $F$ the normalizer of the group $D(F)$ is “closed to be maximal”, we formulate some technical conditions, which imply that the lattice is standard. We also study the conditions concerning the normalizer of $D(R)$ in the case, where $D(R)$ is the elementary subgroup of another Chevalley group $\operatorname{G}(\Psi,R)$ embedded into $\operatorname{G}(\Phi,R)$. 
@article{ZNSL_2019_484_a8,
     author = {R. Lubkov and A. Stepanov},
     title = {Subgroups of {Chevalley} groups over rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--137},
     publisher = {mathdoc},
     volume = {484},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_484_a8/}
}
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R. Lubkov; A. Stepanov. Subgroups of Chevalley groups over rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 484 (2019), pp. 121-137. http://geodesic.mathdoc.fr/item/ZNSL_2019_484_a8/