Abstract
We describe the subgroups of the general linear group GL(n,R) over the field of fractions K of a local principal ideal domain R, containing the group SD(n,R) of diagonal matrices with entries from R and determinant 1. Similar results for overgroups of D(n,R) were obtained earlier by I. Hamdan and N. Vavilov. The results of the present paper generalize also some other known results, especially the description of parahoric subgroups by N. Iwahori and H. Matsumoto. Bibliography: 22 titles.
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