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References
Frank W. Anderson, Kent R. Fuller, Rings and Categories of Modules (Graduate Texts in Mathematics, 13. Springer-Verlag, New York, Heidelberg, Berlin, 1974).
У.А. Белов [Ju.A. Belov], "Н вопросу а решетке нильпотентных многообазий групп нласса 4" [On the question of the lattice of nilpotent varieties of groups of class 4], Algebra i Logika 9 (1970), 623–628; Algebra and Logic 9 (1970), 371–374.
Hermann Boerner, Representations of Groups (North-Holland, Amsterdam, 1963).
Angeline J. Brandt, "The free Lie ring and Lie representations of the full linear group", Trans. Amer. Math. Soc. 56 (1944), 528–536.
R. Brauer and C. Nesbitt, "On the modular characters of groups", Ann. of Math. (2) 42 (1941), 556–590.
Warren Brisley, "Varieties of metabelian p-groups of class p, p+1", J. Austral. Math. Soc. 12 (1971), 53–62.
R.A. Bryce, "Metabelian groups and varieties", Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 281–355.
R.A. Bryce, "Varieties of metabelian p-groups", J. London Math. Soc. (2) 13 (1976), 363–380.
Martin D. Burrow, "Invariants of free Lie rings", Comm. Pure Appl. Math. 11 (1958), 419–431.
Charles W. Curtis, Irving Reiner, Representation Theory of Finite Groups and Associative Algebras (Pure and Applied Mathematics, 11. Interscience [John Wiley & Sons], New York, London, 1962).
K.W. Gruenberg, "Residual properties of infinite soluble groups", Proc. London Math. Soc. (3) 7 (1957), 29–62.
Graham Higman, "Representation of general linear groups and varieties of p-groups", Proc. Internat. Conf. Theory of Groups, Canberra, 1965, 167–173 (Gordon and Breach, New York, London, Paris, 1967).
Bjarni Jónsson, "Varieties of groups of nilpotency three", Notices Amer. Math. Soc. 13 (1966), 488.
А.А. Нлячно [A.A. Kljačko], "Многообразия p-групп малого нласса" [Varieties of p-groups of a small classNOW], Ordered Sets and Lattices No.1, 31–42 (Izdat. Saratov Univ., Saratov, 1971).
А.А. Нлячно [A.A. Kljačko], "Злементы Ли в тензорной алгебре" [Lie elements in a tensor algebra], Sibirsk. Mat. Ž. 15 (1974), 1296–1304, 1430; Siberian Math. J. 15 (1974), 914–921.
L.G. Kovács, M.F. Newman and P.F. Pentony, "Generating groups of nilpotent varieties", Bull. Amer. Math. Soc. 74 (1968), 968–971.
Hans Lausch and Wilfred Nöbauer, Algebra of Polynomials (North-Holland Mathematical Library, 5. North-Holland, Amsterdam, London; American Elsevier, New York, 1973).
Frank Levin, "Generating groups for nilpotent varieties", J. Austral. Math. Soc. 11 (1970), 28–32; Corrigendum, ibid. 12 (1971), 256.
Wilhelm Magnus, "Über Gruppen und zugeordnete Liesche Ringe", J. reine angew. Math. 182 (1940), 142–149.
Wilhelm Magnus, Abraham Karrass, Donald Solitar, Combinatorial Group Theory: Presentations of groups in terms of generators and relations (Pure and Appl. Math. 13. Interscience [John Wiley & Sons], New York, London, Sydney, 1966).
Francis D. Murnaghan, The Theory of Group Representations (The Johns Hopkins Press, Baltimore, 1938).
Hanna Neumann, Varieties of Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967).
Paul Pentony, "Laws in torsion-free nilpotent varieties with particular reference to the laws of free nilpotent groups" (PhD thesis, Australian National University, Canberra, 1970. See also: Abstract: Bull. Austral. Math. Soc. 5 (1971), 283–284).
В.Н. Ремесленников [V. N. Remeslennikov], "Два замечания о З-ступенно нильпотентных группах" [Two remarks on 3-step nilpotent groups], Algebra i Logika Sem. 4 (1965), no. 2, 59–65.
A.G.R. Stewart, "On centre-extended-by-metabelian groups", Math. Ann. 185 (1970), 285–302.
Robert M. Thrall, "A note on a theorem by Witt", Bull. Amer. Math. Soc. 47 (1941), 303–308.
R.M. Thrall, "On symmetrized Kronecker powers and the structure of the free Lie ring", Amer. J. Math. 64 (1942), 371–388.
G.E. Wall, "Lie methods in group theory", these proceedings, 137–173.
Franz Wever, "Operatoren in Lieschen Ringen", J. reine angew. Math. 187 (1949), 44–55.
Franz Wever, "Über Invarianten in Lie'schen Ringen", Math. Ann. 120 (1949), 563–580.
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Kovács, L.G. (1978). Varieties of nilpotent groups of small class. In: Newman, M.F., Richardson, J.S. (eds) Topics in Algebra. Lecture Notes in Mathematics, vol 697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103131
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DOI: https://doi.org/10.1007/BFb0103131
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