Journal of Mathematical Sciences

, Volume 95, Issue 2, pp 2065–2069 | Cite as

Garlands containing the general linear group over an intermediate field

  • Z. I. Borevich
  • V. A. Koibaev
  • I. V. Lavrent'ev


Let K/k be a finite extension of fields with an intermediate subfield L, and let H = GLL(K) be the general linear group of all L-linear invertible mappings of the vector space of the field K over L. It is proved that the subgroups lying between GLK(K)H and the normalizer of H in G, where G = GLk(K), form a garland. Bibliography: 4 titles.


Vector Space Linear Group General Linear Group Finite Extension Invertible Mapping 
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  1. 1.
    A. H. Al-Hamad,Garlands in Linear Groups Related to Valuation Rings, Ph.D. thesis, St. Petersburg (1992).Google Scholar
  2. 2.
    E. Artin,Geometric Algebra, Interscience, New York (1957).Google Scholar
  3. 3.
    V. A. Koibaev, “The normalizer of the automorphism group of a module associated with an extension of the basic ring,”Zap. Nauchn. Semin. POMI,211, 136–145 (1994).Google Scholar
  4. 4.
    D. A. Suprunenko,Matrix Groups [in Russian], Nauka, Moscow (1972).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • Z. I. Borevich
  • V. A. Koibaev
  • I. V. Lavrent'ev

There are no affiliations available

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