Subgroups of SLn over a semilocal ring

Abstract

In the present paper, it is proved that if R is a commutative semilocal ring all the residue fields of which contain at least 3n + 2 elements, then for every subgroup H of the special linear group SL(n, R), n ≥ 3, containing the diagonal subgroup SD(n, R) there exists a unique D-net σ of ideals of R such that Γ(σ)≤H≤NΓ(σ). In works by Z. I. Borewicz and the author, similar results were established for GL n over semilocal rings and for SL n over fields. Later I. Hamdan obtained a similar description for the very special case of uniserial rings. Bibliography: 76 titles.