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The Borevich theorem for the hyperbolic unitary group over a skew field

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Abstract

We complete a series of papers where we prove that the lattice of overdiagonal subgroups in the hyperbolic unitary group over a skew field admits the standard description. We consider a skew field of characteristic 2 with involution of the first kind. A form parameter differs from the minimal one. Bibliography: 13 titles.

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References

  1. Z. I. Borevich, “Description of subgroups of the general linear group that contain the group of diagonal matrices,” Zap. Nauchn. Semin. LOMI, 64, 12–29 (1976).

    MATH  Google Scholar 

  2. Z. I. Borevich and N. A. Vavilov, “Subgroups of the general linear group over a semilocal ring containing the group of diagonal matrices,” Trudy Steklov Mat. Inst., 148, 43–57 (1978).

    MathSciNet  MATH  Google Scholar 

  3. N. A. Vavilov, “On subgroups of the general linear group over a semilocal ring that contain the group of diagonal matrices,” Vestn. Leningr. Univ., 1, 10–15 (1981).

    MATH  MathSciNet  Google Scholar 

  4. E. V. Dybkova, “On net subgroups in the hyperbolic unitary group,” Algebra Analiz, 9, 79–86 (1997).

    MATH  MathSciNet  Google Scholar 

  5. E. V. Dybkova, “On the conjugacy of net subgroups in the hyperbolic unitary group over a field,” Vestn. St.Petersburg Univ. Ser. Mat. Mekh. Astr., 4, 4, 10–12 (1997).

    MATH  Google Scholar 

  6. E. V. Dybkova, “Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field,” Zap. Nauchn. Semin. POMI, 236, 87–96 (1997).

    MATH  Google Scholar 

  7. E. V. Dybkova, “Form nets and the lattice of overdiagonal subgroups of the symplectic group over a field of characteristic 2,” Algebra Analiz, 10, 113–129 (1998).

    MATH  MathSciNet  Google Scholar 

  8. E. V. Dybkova, “On overdiagonal subgroups of the hyperbolic unitary group for a skew field,” Zap. Nauchn. Semin. POMI, 289, 154–206 (2002).

    MATH  Google Scholar 

  9. E. V. Dybkova, “Overdiagonal subgroups of the hyperbolic unitary group for the good form ring over a skew field,” Zap. Nauchn. Semin. POMI, 305, 121–135 (2003).

    Google Scholar 

  10. A. Bak and N. Vavilov, “Structure of hyperbolic unitary groups. I. Elementary subgroups,” Algebra Colloq., 7:2, 159–196 (2000).

    MathSciNet  MATH  Google Scholar 

  11. J. Dieudonné, “On the structure of unitary groups,” Trans. Amer. Math. Soc., 72, 367–385 (1952).

    Article  MATH  MathSciNet  Google Scholar 

  12. A. J. Hahn and O. T. O’Meara, The Classical Groups and K-Theory, Springer, Berlin (1989).

    MATH  Google Scholar 

  13. W. M. Pender, “Classical groups over division rings of characteristic two,” Bull. Austral. Math. Soc., 7, 191–226 (1972).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    E. V. Dybkova

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  1. E. V. Dybkova
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 136–167.

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Dybkova, E.V. The Borevich theorem for the hyperbolic unitary group over a skew field. J Math Sci 136, 3908–3925 (2006). https://doi.org/10.1007/s10958-006-0209-4

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  • DOI: https://doi.org/10.1007/s10958-006-0209-4

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