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Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields

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Abstract

Given the ring of integers O K of an algebraic number field K, for which natural numbers n there exists a finite group G ⊂ GL(n, O K ) such that O K G, the O K -span of G, coincides with M(n, O K ), the ring of (n × n)-matrices over O K ? The answer is known if n is an odd prime. In this paper we study the case n = 2; in the cases when the answer is positive for n = 2, for n = 2m there is also a finite group G ⊂ GL(2m, O K ) such that O K G = M(2m, O K ).

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, Seminargebäude A5, 68131, Mannheim, Germany

    Dmitry Malinin

  2. Department of Mathematics & Computer Science, University of Antwerp, Middelheim campus, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Freddy Van Oystaeyen

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  1. Dmitry Malinin
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  2. Freddy Van Oystaeyen
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Correspondence to Dmitry Malinin.

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Malinin, D., Van Oystaeyen, F. Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields. Algebr Represent Theor 14, 201–211 (2011). https://doi.org/10.1007/s10468-009-9184-z

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