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Journal of Mathematical Sciences

, Volume 171, Issue 3, pp 307–316 | Cite as

Parabolic subgroups of SL n and Sp2l over a Dedekind ring of arithmetic type

  • A. V. Alexandrov
  • N. A. Vavilov
Article
  • 23 Downloads

Let R be a commutative ring all of whose proper factor rings are finite and in which a unit of infinite order exists. It is shown that for a subgroup P in G =SL(n, R), n ≥3,or in G =Sp(2l, R), l ≥2, containing the standard Borel subgroup B, the following alternative holds: either P contains a relative elementary subgroup EI for some ideal I≠0 or H is contained in a proper standard parabolic subgroup. For Dedekind rings of arithmetic type, this allows one, under some mild additional assumptions on units, to completely describe the overgroups of B in G. Bibliography: 30 titles.

Keywords

Russia Additional Assumption Commutative Ring Parabolic Subgroup Borel Subgroup 
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© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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