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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.
MSC:
20G25 Linear algebraic groups over local fields and their integers
20E07 Subgroup theorems; subgroup growth
20E15 Chains and lattices of subgroups, subnormal subgroups
Keywords:
net subgroups
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