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On division rings generated by polycyclic groups

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Abstract

LetD=F(G) be a division ring generated as a division ring by its central subfieldF and the polycyclic-by-finite subgroupG of its multiplicative group, letn be a positive integer and letX be a finitely generated subgroup of GL(n, D). It is implicit in recent works of A. I. Lichtman thatX is residually finite. In fact, much more is true. If charD=p≠0, then there is a normal subgroup ofX of finite index that is residually a finitep-group. If charD=0, then there exists a cofinite set π=π(X) of rational primes such that for eachp in π there is a normal subgroup ofX of finite index that is residually a finitep-group.

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Authors and Affiliations

  1. Department of Pure Mathematics, Queen Mary College, E1 4NS, London, England

    B. A. F. Wehrfritz

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  1. B. A. F. Wehrfritz
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Wehrfritz, B.A.F. On division rings generated by polycyclic groups. Israel J. Math. 47, 154–164 (1984). https://doi.org/10.1007/BF02760514

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