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Configuration of subgroups in the special linear group over a skew field with infinite center

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Abstract

Let T be a skew field with infinite center, let Γ be the special linear group over T of degree ≥ 3, and let Δ be the subgroup of diagonal matrices with unit Dieudonee determinant. It is proved that for each intermediate subgroup H, Δ ≤ H ≤ Γ, there exists a net σ of order n such that Γ(σ ≤ H ≤ N(σ).

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Authors
  1. Bui Suan Khai
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 5–12, 1989.

In conclusion, the author would like to thank his instructor Z. I. Borevich, as well as N. A. Vavilov, for their assistance.

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Khai, B.S. Configuration of subgroups in the special linear group over a skew field with infinite center. J Math Sci 57, 3449–3452 (1991). https://doi.org/10.1007/BF01100111

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