We present sufficient conditions for an isomorphic representation over a field of a group by matrices. A criterion of the matrix representation for finitely generated groups is given. Bibliography: 7 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. I. Mal’tsev (Mal’cev), “On the faithful representation of infinite groups by matrices” [in Russian], Mat. Sb. 8, No. 3, 405–423 (1940); English transl.: Am. Math. Soc. Transl. Ser. 2 45, 1–18 (1965).
B. A. F. Wehrfritz, Infinite Linear Groups, Springer, Berlin (1973).
V. L. Nisnevich, “On groups isomorphically representable by matrices over a commutative field” [in Russian], Mat. Sb. 8, No. 3, 395–403 (1940).
Yu. I. Merzlyakov, Rational Groups [in Russian], Nauka, Moscow (1980).
A. Lubotzky, “A group-theoretic characterization of linear groups,” J. Algebra 113, 207–214 (1988).
Yu. L. Ershov, Multivalued Fields [in Russian], Nauchnaya Kniga (IDMI), Novosibirsk (2000); English transl.: Kluwer Acad., New York (2001).
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publ., London etc. (1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 11, No. 2, 2011, pp. 21–26
Rights and permissions
About this article
Cite this article
Bryukhanov, O.V. Approximation properties and linearity of groups. J Math Sci 188, 354–358 (2013). https://doi.org/10.1007/s10958-012-1133-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-012-1133-4