Journal of Mathematical Sciences

, Volume 147, Issue 5, pp 6995–7004

Subgroups of SLn over a semilocal ring


DOI: 10.1007/s10958-007-0525-3

Cite this article as:
Vavilov, N.A. J Math Sci (2007) 147: 6995. doi:10.1007/s10958-007-0525-3


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 GLn over semilocal rings and for SLn over fields. Later I. Hamdan obtained a similar description for the very special case of uniserial rings. Bibliography: 76 titles.

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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