Subgroups of orthogonal groups in even dimensions over a local field

The description of the subgroups of the orthogonal linear groups SO(2l,K) and GO(2l,K) over the field of fractions K of a local principal ideal domain R that contain the maximal split torus T = T(2l,R) with entries from R is presented. A similar result for overgroups of T in the case of a semilocal ring and a field was obtained earlier by N. Vavilov. The result of the present paper generalizes some known results as well. Bibliography: 15 titles. ©2006 Springer Science+Business Media, Inc.