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Subgroups of the orthogonal groups of even degree over a local field. (Russian, English) Zbl 1082.20027
Zap. Nauchn. Semin. POMI 321, 240-250 (2005); translation in J. Math. Sci., New York 136, No. 3, 3966-3971 (2006).
Summary: We obtain the description of subgroups of orthogonal linear groups \(\text{SO}(2l,K)\) and \(\text{GO}(2l,K)\) over the field of fractions \(K\) of a principal ideal domain \(R\) containing the maximal split tori \(T=T(2l,R)\) with entries from \(R\). Similar results for overgroups \(T\) in case of a semilocal ring and field were obtained earlier by N. Vavilov. The results of the present paper generalize also some known results.
20G25 Linear algebraic groups over local fields and their integers
20E07 Subgroup theorems; subgroup growth
20E15 Chains and lattices of subgroups, subnormal subgroups
net subgroups
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