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The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

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Abstract

LetD be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure ofD x (the multiplicative group ofD) can be reduced to questions about finite quotients ofD x. In this paper we prove that when deg(D)=3, finite quotients ofD x are solvable. the proof uses Wedderburn’s Factorization Theorem.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat Gan, 52900, Israel

    L. H. Rowen

  2. Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

    Y. Segev

Authors
  1. L. H. Rowen
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  2. Y. Segev
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Corresponding author

Correspondence to L. H. Rowen.

Additional information

Partially supported by grant no. 427-97-1 from the Israeli Science Foundation and by grant no. 6782-1-95 from the Israeli Ministry of Science and Art.

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Rowen, L.H., Segev, Y. The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable. Isr. J. Math. 111, 373–380 (1999). https://doi.org/10.1007/BF02810692

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  • DOI: https://doi.org/10.1007/BF02810692

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