Abstract
We describe solvable groups all proper quotient groups of which possess layer-Chernikov properties.
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References
M. F. Newman, “On a class of metabelian groups,” Proc. London Math. Soc., 10, No. 39, 354–364 (1960).
M. F. Newman, “On a class of nilpotent groups,” Proc. London Math. Soc., 10, No. 39, 365–375 (1960).
D. McCarthy, “Infinite groups whose proper quotients are finite,” Commun. Pure Appl. Math., 21, No. 5, 157–167 (1968).
D. McCarthy, “Infinite groups whose proper quotients are finite,” Commun. Pure Appl. Math., 21, No. 6, 545–562 (1968).
J. S. Wilson, “Groups with every proper quotients finite,” Proc. Cambr. Phil. Soc., 69, No. 3, 373–391 (1972).
D. J. S. Robinson and J. S. Wilson, “Soluble groups with many polycyclic quotients,” Proc London Math. Soc., 48, 193–229 (1984).
L. A. Kurdachenko, V. E. Goretskii, and V. V. Pylaev, “Groups with a certain system of minimax quotient groups,” Dopov. Akad. Nauk Ukr. RSR, Ser. A, No. 3, 17–20 (1988).
S. Franciosi and F. de Giovanny, “Soluble groups with many Chernikov quotients,” Atti Accad. Naz. Lincei, 79, 19–24 (1985).
D. J. S. Robinson and Z. Zhang, “Groups whose proper quotients have finite derived subgroups,” J. Algebra, 118, No. 2, 346–368 (1988).
S. N. Chernikov, “Infinite layer-finite groups,” Mat. Sb., 22, No. 1, 101–133 (1948).
R. Baer, “Finiteness properties of groups,” Duke Math. J., 15, No. 4, 1021–1032 (1948).
S. N. Chernikov, “On layer-finite groups,” Mat. Sb., 45, 415–416 (1958).
Ya. D. Polovitskii, “Layer-extremal groups,” Mat. Sb., 56, No. 1, 95–106 (1962).
Ya. D. Polovitskii, “Local-extremal and layer-extremal groups,” Mat. Sb., 58, No. 6, 685–694 (1962).
D. J. S. Robinson, “On the theory of groups with extremal layers,” J. Algebra, 14, 182–193 (1970).
L. S. Kazarin and L. A. Kurdachenko, “Finiteness and factorization conditions in infinite groups,” Usp. Mat. Nauk, 47, No. 3, 75–114 (1992).
Yu. M. Gorchakov, Groups with Finite Classes of Conjugate Elements [in Russian], Nauka, Moscow (1978).
D. I. Zaitsev, “Decomposable extensions of Abelian groups,” in: Structure of Groups and Properties of Their Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Science, Kiev (1986), pp. 22–31.
J. S. Wilson, “Some properties of groups inherited by normal subgroups of finite index,” Math. Z., 114, No. 1, 19–21 (1970).
C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience (1962).
D. I. Zaitsev, “On the existence of direct complements in groups with operators,” in: Investigations in the Theory of Groups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1970), pp. 26–44.
S. N. Chernikov, “On the structure of groups with finite classes of conjugate elements,” Dokl. Akad. Nauk SSSR, 115, 60–63 (1957).
R. Baer, “Irreducible groups of automorphisms of Abelian groups,” Pacif J. Math., 14, No. 2, 385–406 (1964).
M. J. Karbe and L. A. Kurdachenko, “Just infinite modules over locally soluble groups,” Archiv Math., 51, No. 5, 401–411 (1988).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.50, No. 11, pp. 1497–1505, November, 1998.
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Kalashnikova, N.V. Groups all proper quotient groups of which possess layer-Chernikov properties. Ukr Math J 50, 1710–1718 (1998). https://doi.org/10.1007/BF02524477
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DOI: https://doi.org/10.1007/BF02524477