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Intermediate subgroups in the unitary group over the skew field of quaternions

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Abstract

We give a description of the lattice of those subgroups of the unitary group over the skew field of quaternions which contain the diagonal matrices (intermediate subgroups). It is shown that this lattice is finite. A condition for conjugacy of intermediate subgroups is found.

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Literature cited

  1. Z. I. Borevich, “The position of subgroups,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,94, 5–12 (1979).

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  2. Z. I. Borevich and S. L. Krupetskii, “Subgroups of the unitary group containing the group of diagonal matrices,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,86, 19–29 (1979).

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  3. S. L. Krupetskii, “Subgroups of the unitary group over a local field,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,94, 81–103 (1979).

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Authors
  1. S. L. Krupetskii
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 96–101, 1982.

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Krupetskii, S.L. Intermediate subgroups in the unitary group over the skew field of quaternions. J Math Sci 26, 1894–1897 (1984). https://doi.org/10.1007/BF01670576

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  • DOI: https://doi.org/10.1007/BF01670576

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