Literature cited
K. Chevallé, Group Theory [Russian translation], Vol. 2, IL (1958).
A. Borel, “Groupes linéaires algébriques,” Ann. Math.,64, No. 1, 20–82 (1956).
Yu. I. Merzlyakov, Rational Groups [in Russian], Vol. 1, Novosibirsk (1967).
Kh. Neiman, Varieties of Groups [in Russian], Mir (1969).
B. I. Plotkin, Groups of Automorphisms of Algebraic Systems [in Russian], Mir (1966).
I. N. Sanov, “A property of a representation of a free group,” Dokl. Akad. Nauk SSSR,57, No. 7, 657–659 (1947).
W. Magnus, “On a theorem of Marshall Hall,” Ann. Math.,40 (2), No. 4, 764–768 (1939).
V. M. Kopytov, “Representations of finitely generated groups by matrices,” Sibirsk. Mat., Zh.,11, No. 1, 91–102 (1970).
V. P. Platonov, “Linear groups with identity relations,” Dokl. Akad. Nauk SSSR,11, No. 7, 581–582 (1967).
A. I. Mal'tsev, “An isomorphism of a representation of infinite groups by matrices,” Matem. Sb.,8, No. 3, 405–422 (1940).
K. K. Andreev, “Nilpotent groups and Lie algebras,” Algebra i Logika,7, No. 4, 4–14 (1968).
K. K. Andreev, “Nilpotent groups and Lie Algebras. 2,” Algebra i Logika,8, No. 6, 625–635 (1969).
A. L. Shmel'kin, “Interlacing and varieties of groups,” Izv. Akad. Nauk SSSR, Ser. Matem.,29, No. 1, 149–170 (1965).
A. L. Shmel'kin, “Free polynilpotent groups,” Izv. Akad. Nauk SSSR, Ser. Matem.,28, No. 1, 91–122 (1964).
F. Hall, “Nilpotent groups,” Mathematica,12, No. 1, 3–36 (1968).
Yu. A. Bakhturin, “Two notes on varieties of Lie algebras,” Matem. Zametski,4, No. 4, 387–398 (1968).
E. Witt, “Treue Darstellung Liescher Ringe,” J. Reine Angew. Math., 177, 152–160 (1937).
N. Jacobson, Lie Algebras [Russian translation], Mir (1964).
A. I. Mal'tsev, “Algebras with identity-defining relations,” Matem. Sb.,26, No. 1, 19–33 (1950).
Additional information
Translated from Algebra i Logika, Vol. 10, No. 4, pp. 449–473, July–August, 1971.
Rights and permissions
About this article
Cite this article
Éidel'kind, D.I. Exact representations for free groups. Algebr Logic 10, 281–296 (1971). https://doi.org/10.1007/BF02219814
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02219814