Abstract
We present a structural description of free groups and some critical subgroups of a given variety.
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REFERENCES
O. N. Golovin and N. P. Gol'dina, “Subgroups of free metabelian groups,” Mat. Sb., 37, 323–336 (1955).
N. F. Sesekin, “On classification of torsion-free metabelian groups with finitely many generators,” Uchen. Zap. Ural. Univ., 19, 27–51 (1956).
P. Conrad, “Skew tensor products and groups of class two,” Nagoya Math. J., 23, 15–51 (1963).
V. N. Remeslennikov, “Two remarks on nilpotent groups of class 3,” Algebra Logika (Seminar), 4, No. 2, 59–65 (1965).
F. Haimo, “Power type endomorphisms of some class 2 groups,” Pacif. J. Math., 5, 201–213 (1955).
B. Jonsson, “Varieties of groups of nilpotence three,” Notic. Amer. Math. Soc., 13, No. 4, 488 (1966).
F. Levi, “Groups in which the commutator operation satisfies certain algebraic conditions,” J. Indian Math. Soc., 6, 87–97 (1942).
A. I. Shirshov, “On some groups close to Engel groups,” in: Rings and Algebras [in Russian], Nauka, Moscow (1984), pp. 106–114.
H. Neumann, Varieties of Groups [Russian translation], Mir, Moscow (1969).
G. Higman, “Some remarks on varieties of groups,” Quart. J. Math., 165–178 (1959).
D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, Vol. 2, Springer, Berlin (1972).
A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
M. Hall, Jr., The Theory of Groups [Russian translation], Inostrannaya Literatura, Moscow (1962).
Cher Ving, “On finite p-groups with cyclic commutator subgroups,” Arch. Math., 39, No. 4, 295–298 (1982).
M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1982).
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Mel'nyk, T.I. Varieties of Groups with Invariant Centralizers of Subgroups. Ukrainian Mathematical Journal 54, 592–602 (2002). https://doi.org/10.1023/A:1021083211071
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DOI: https://doi.org/10.1023/A:1021083211071