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Subgroups of Chevalley groups of types $B_l$ and $C_l$ containing the group over a subring and corresponding carpets

We continue study of subgroups of a Chevalley group $G_P(Φ,R)$ over a ring $R$ with a root system $Φ$ and a weight lattice $P$, containing the elementary subgroup $E_P(Φ,K)$ over a subring $K$ of $R$. Recently A. Bak and A. Stepanov considered the symplectic case (i. e. the case of simply connected group of type $Φ=C_l$) in characteristic 2. In this article we extend their result for groups with arbitrary weight lattice of types $B_l$ and $C_l$. Similarly to the work of Nuzhin that handles the case of an algebraic extension $R$ of a nonperfect field $K$ of bad characteristic, we use in the description a special kind of carpet subgroups. In the second half of the article we study Bruhat and Gauss decompositions for these carpet subgroups.

preprint2020arXivOpen access

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