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Zbl 0820.20055
Pink, Richard
Classification of pro-$p$ subgroups of $\text{SL}\sb 2$ over a $p$-adic ring, where $p$ is an odd prime. (English)
[J] Compos. Math. 88, No.3, 251-264 (1993). ISSN 0010-437X; ISSN 1570-5846/e

Let $A$ be a semilocal ring and $I$ be the intersection of its maximal ideals, such that $A$ is compact with respect to the $I$-adic topology, and $A/I$ is annihilated by a prime $p\ne 2$. A convenient description for all pro-$p$-subgroups $\Gamma\subset\text{SL}\sb 2(A)$ is given and a corollary on descending central and derived series of $\Gamma$ is extracted.
[Yu.N.Mukhin (Ekaterinburg)]

MSC 2000:: *20G35 Linear algebraic groups over adèles and other rings and schemes
20E18 Profinite groups
20E07 Subgroup theorems (group theory)
20F14 Series of groups and generalizations

Keywords: central series; derived series; semilocal rings; pro-$p$-subgroups

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