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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
net subgroups
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