Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

The structure of subnormal subgroups of symplectic groups over local rings

  • 19 Accesses

  • 1 Citations

Abstract

We give a description of subnormal subgroups of a symplectic group over a local ring with invertible element 2. We also propose a description of subgroups of this group normalized by special congruence subgroups.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Tazhetdinov S., “Subnormal structure of symplectic groups over local rings,” Mat. Zametki, 37, No. 2, 289–298 (1985).

  2. 2.

    Klingenberg W., “Symplectic groups over local rings,” Amer. J. Math., 85, No. 2, 232–240 (1963).

  3. 3.

    McDonald B. R., Geometric Algebra over Local Rings, Marcel Dekker, Inc., New York (1976).

  4. 4.

    Kirkwood B. and McDonald B. R., “The symplectic group over a ring with one in its stable range,” Pacific J. Math., 92, No. 1, 111–125 (1981).

  5. 5.

    Tazhetdinov S., “Subnormal structure of two-dimensional linear groups over rings that are close to fields,” Algebra and Logic, 24, No. 4, 269–277 (1985).

  6. 6.

    Tazhetdinov S., “Subnormal structure of symplectic groups over (2, 3)-full rings,” Siberian Math. J., 34, No. 6, 1149–1153 (1993).

  7. 7.

    Arrell D. G., “The subnormal subgroup structure of the infinite symplectic group,” Proc. Edinburgh Math. Soc., 25, No. 3, 209–216 (1982).

  8. 8.

    Tazhetdinov S., “Subnormal structure of two-dimensional linear groups over full rings,” Mat. Zametki, 71, No. 6, 924–930 (2002).

Download references

Author information

Additional information

Original Russian Text Copyright © 2006 Tazhetdinov S.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 665–669, May–June, 2006.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tazhetdinov, S. The structure of subnormal subgroups of symplectic groups over local rings. Sib Math J 47, 551–554 (2006). https://doi.org/10.1007/s11202-006-0066-x

Download citation

Keywords

  • subnormal subgroup
  • congruence subgroup
  • symplectic group
  • local ring
  • symplectic transvection