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Proceedings of the American Mathematical Society

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A note on free products of linear groups

Author: Zbigniew S. Marciniak
Journal: Proc. Amer. Math. Soc. 94 (1985), 46-48
MSC: Primary 20G15; Secondary 20E06
MathSciNet review: 781053
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Abstract: For a field $ K$, let $ \bar K$ denote its algebraic closure. Assume that $ \left\vert {\bar K:K} \right\vert = \infty $. Then for any linear groups $ G,{\text{ }}H \subseteq {\text{G}}{{\text{L}}_n}(K)$ their free product $ G * H$ can be embedded into $ {\text{G}}{{\text{L}}_N}(K(t))$. Here $ N$ is an integer depending on $ K$ only and $ t$ stands for an indeterminate.

References [Enhancements On Off] (What's this?)

  • [1] S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 0197234 (33:5416)
  • [2] P. B. Shalen, Linear representations of amalgamated products, J. Pure Appl. Algebra 15 (1979), 87-97. MR 535185 (80e:20011)
  • [3] B. A. F. Wehrfritz, Infinite linear groups, Queen Mary College, London, 1969. MR 837425

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