Journal of Soviet Mathematics

, Volume 17, Issue 4, pp 1951–1959 | Cite as

Subgroups of the unitary group that contain the group of diagonal matrices

  • Z. I. Borevich
  • S. L. Krupetskii

Abstract

In the groupU(n,ℂ) of all complex unitary matrices we obtain a description of the lattice of those subgroups H that contain the group of diagonal unitarymatrices. This lattice is finite, and the connected intermediate subgroups H are in bijective correspondence with the equivalence relations on a set ofn elements.

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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).Google Scholar
  2. 2.
    Kh. D. Ikramov, A Book of Problems in Linear Algebra [in Russian], Nauka, Moscow (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Z. I. Borevich
  • S. L. Krupetskii

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