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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1985-0781053-X
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.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0781053-X
Article copyright: © Copyright 1985 American Mathematical Society