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Proceedings of the American Mathematical Society

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On subgroups of the multiplicative group of skew fields

Author: A. Lichtman
Journal: Proc. Amer. Math. Soc. 63 (1977), 15-16
MSC: Primary 20H20; Secondary 16A18
MathSciNet review: 0447432
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Abstract: We give an example of a skew field D for which the multiplicative group $ {D^ \ast }$ of D contains a finitely generated subgroup which satisfies a nontrivial identity and has no solvable normal subgroup of finite index. It gives a negative answer to a question of S. Bachmuth.

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  • [1] J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250–270. MR 0286898
  • [2] M. F. Newman (ed.), Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Mathematics, Vol. 372, Springer-Verlag, Berlin-New York, 1974. Held at the Australian National University, Canberra, August 13–24, 1973; With an introduction by B. H. Neumann. MR 0344315
  • [3] A. I. Lichtman, On embedding of group rings in division rings, Israel J. Math. 23 (1976), no. 3-4, 288–297. MR 0432692
  • [4] D. J. S. Robinson, Finiteness conditions and generalized soluble groups, Vols. 1, 2, Springer-Verlag, Berlin and New York, 1972. MR 48 #11314, 11315.
  • [5] Gilbert Baumslag, Wreath products and extensions, Math. Z. 81 (1963), 286–299. MR 0151518

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Keywords: Multiplicative group of division ring, group ring
Article copyright: © Copyright 1977 American Mathematical Society