2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78121A complete description of subgroups in the general linear group over a semilocal ring containing the group of diagonal matrices was obtained by Z.I.Borewicz and N.A.Vavilov. It is shown in the present paper that a similar description holds for the intermediate subgroups of the group of all automorphisms of the lattice of right submodules of a free finite rank R-module over a simple Artinian ring containing the group consisting of those automorphisms which leave invariant an appropriate sublattice.AmsTeX, 6 pages, compile twice; revised version of the Bielefeld preprint 99-008Rings and AlgebrasGroup Theory11H56; 20E15; 20G15; 20G35; 03G10; 20E07text