Abstract
We introduce the notion of non-Abelian sectional rank of a group and study locally nilpotent non-Abelian groups of finite non-Abelian sectional rank. It is proved that the (special) rank of these groups is finite.
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O. Yu. Dashkova, “Solvable groups of finite non-Abelian rank,”Ukr. Mat. Zh.,42, No. 2, 159–164 (1990).
O. Yu. Dashkova, “Locally almost solvable groups of finite non-Abelian rank,”Ukr. Mat. Zh.,42, No. 4, 447–482 (1990).
Yu. M. Gorchakov, “On the existence of Abelian subgroups of infinite rank in locally solvable groups,”Dokl. Akad. Nauk SSSR,156, No. 1, 17–20 (1964).
N. N. Myagkova, “Groups of finite rank,”Izv. Akad. Nauk SSSR, Ser. Mat.,13, No. 6, 495–512 (1949).
S. N. Chernikov, “Finiteness conditions in the general theory of groups,”Usp. Mat. Nauk,14, No. 5, 45–96 (1959).
D. J. S. Robinson,A Course in the Theory of Groups, Springer, New York (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 452–455, April, 1995.
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Dashkova, O.Y. Locally nilpotent groups of finite non-Abelian sectional rank. Ukr Math J 47, 524–527 (1995). https://doi.org/10.1007/BF01056037
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DOI: https://doi.org/10.1007/BF01056037