Geodesic
Overgroups of Levi subgroups I. The case of abelian unipotent radical
Algebra i analiz, Tome 31 (2019) no. 6, pp. 79-121.

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In the present paper, sandwich classification is established for the overgroups of the subsystem subgroup $ E(\Delta ,R)$ of the Chevalley group $ G(\Phi ,R)$ for the three types of the pair $ (\Phi ,\Delta )$ (the root system and its subsystem) listed below such that the group $ G(\Delta ,R)$ is (up to a torus) a Levi subgroup of the parabolic subgroup with Abelian unipotent radical. Namely, it is shown that for any overgroup $ H$ of this sort, there exists a unique pair of ideals $ \sigma $ of the ring $ R$ with $ E(\Phi ,\Delta ,R,\sigma )\le H\le N_{G(\Phi ,R)}(E(\Phi ,\Delta ,R,\sigma ))$.
Keywords: Chevalley groups, commutative rings, half-spinor group, exceptional groups, Levi subgroup, subgroup lattice, nilpotent structure of K1. 
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P. B. Gvozdevsky. Overgroups of Levi subgroups I. The case of abelian unipotent radical. Algebra i analiz, Tome 31 (2019) no. 6, pp. 79-121. http://geodesic.mathdoc.fr/item/AA_2019_31_6_a2/

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