Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Some subgroups of the full linear group

  • 18 Accesses

  • 4 Citations

Abstract

Further observations are made on the author's earlier paper (Ref. Zh. Mat., 1977, 5A284) dealing with the lattice H of all subgroups of the full linear group GL(n, K) over a field K that contain the group K of diagonal matrices. It is noted, for example, that for an infinite field K all subgroups inD(n, K) are algebraic; a subgroup in H is connected if and only if it is a net subgroup; the lattice of all connected subgroups in H is isomorphic to the lattice of all marked topologies onn points; any subgroup H in H is a semidirect product H=A·Ho of a maximal connected normal subgroup Ho of H and a finite group A of, permutation matrices.

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

Literature cited

  1. 1.

    Z. I. Borevich, “A description of the subgroups of the full linear group that contain the group of diagonal matrices,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,64, 12–29 (1976).

  2. 2.

    Z. I. Borevich and N. A. Vavilov, “Subgroups of the full linear group over a scalarsemilocal ring that contain the group of diagonal matrices,” Tr. Mat. Inst. Akad. Nauk SSSR,148 (1977).

  3. 3.

    V. A. Koibaev, “Examples of nonmonomial linear groups without transvections,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,71, 153–154 (1977).

Download references

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 42–46, 1977.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Borevich, Z.I. Some subgroups of the full linear group. J Math Sci 20, 2528–2532 (1982). https://doi.org/10.1007/BF01681469

Download citation

Keywords

  • Normal Subgroup
  • Finite Group
  • Early Paper
  • Linear Group
  • Diagonal Matrice