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Normal structure of the unitary group over a local ring

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Abstract

A new approach is used to describe the normal subgroups of unitary groups over the ring of integers of an unramified quadratic extension of a local field of characteristic ≠2. This method is based on the author's results concerning subgroups of unitary groups normalized by diagonal unitary matrices. By means of this method it has been possible to remove restrictions imposed by other authors in a number of papers pertaining to the same question.

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Literature cited

  1. Z. I. Borevich, “Arrangement of subgroups,” J. Sov. Math.,19, No. 1 (1982).

  2. I. Z. Golubchik, “Normal subgroups of the orthogonal group over a ring with involution,” Usp. Mat. Nauk,30, No. 6, 165 (1975).

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  3. S. L. Krupetskii, “Subgroups of the unitary group over a local field,” J. Sov. Math.,19, No. 1 (1982).

  4. S. L. Krupetskii, “Subgroups of the unitary group over a dyadic local field,” J. Sov. Math.,24, No. 4 (1984).

  5. S. L. Krupetskii, “Subgroups of a nonclassical unitary group over a local field,” in: VII All-Union Symposium on Group Theory, Abstracts of Reports, Krasnoyarsk (1980), p. 57.

  6. S. L. Krupetskii, “Arrangement of subgroups in unitary groups,” Candidate's Dissertation, Physical and Mathematical Sciences, Leningrad University (1980).

  7. C.-N. Chang, “The unitary group over the integers of an unramified local field,” J. Algebra,30, No. 3, 535–547 (1974).

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  8. D. G. James, “Unitary groups over local rings,”` J. Algebra,52, No.2, 354–363 (1978).

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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. 114, pp. 150–163, 1982.

The results in this paper were obtained by the author while he was a post-graduate student under the direction of Z. I. Borevich. The author would like to express his sincere gratitude to Professor Borevich.

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Krupetskii, S.L. Normal structure of the unitary group over a local ring. J Math Sci 27, 2944–2954 (1984). https://doi.org/10.1007/BF01410748

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  • DOI: https://doi.org/10.1007/BF01410748

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