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Parabolic congruence subgroups in linear groups

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Abstract

Parabolic subgroups are described for the full and special linear groups over a commutative ring R which contain a principal congruence level a, where a is an ideal of R such that R/a is semilocal. It is assumed that R is generated additively by its invertible elements and that the ring identity can be expressed as a sum of two invertible elements.

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Literature cited

  1. Z. I. Borevich, “On parabolic subgroups of linear groups over a semilocal field,” Vestn. Leningr. Univ., No. 13, 16–24 (1976).

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  2. Z. I. Borevich, “On parabolic subgroups in the special linear group over a semilocal field,” Vestn. Leningr. Univ., No. 19 (1976).

  3. N. S. Romanovskii, “Subgroups of the general and special linear groups over a ring,” Mat. Zametki,9, No. 6, 699–708 (1971).

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Authors
  1. N. A. Vavilov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 55–63, 1976.

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Vavilov, N.A. Parabolic congruence subgroups in linear groups. J Math Sci 17, 1748–1754 (1981). https://doi.org/10.1007/BF01091760

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  • DOI: https://doi.org/10.1007/BF01091760

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