Geodesic
Subgroups of $\operatorname{SL}_n$ over a semilocal ring
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 33-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper we prove that if $R$ is a commutative semi-local ring all of whose residue fields contain at least $3n+2$ elements, then for every subgroup $H$ of the special linear group $\operatorname{SL}(n,R)$, $n\ge 3$, containing the diagonal subgroup $\operatorname{SD}(n,R)$ there exists a unique $D$-net $\sigma$ of ideals $R$ such that $\mathrm{G}(\sigma)\le H\le N_{\mathrm{G}}(\sigma)$. In the works by Z. I. Borewicz and the author similar results were established for $\operatorname{GL}_n$ over semi-local rings and for $\operatorname{SL}_n$ over fields. Later I. Hamdan obtained similar description for a very special case of uniserial rings. 
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N. A. Vavilov. Subgroups of $\operatorname{SL}_n$ over a semilocal ring. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 33-53. http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a1/

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