Abstract
We study non-Abelian locally finite groups and non-Abelian locally solvable groups of finite non-Abelian sectional rank and prove that their (special) rank is finite.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. Yu. Dashkova, “Locally nilpotent groups of finite non-Abelian sectional rank”, Ukr. Mat. Zh., 47, No. 4, 452–455 (1995).
O. Yu. Dashkova, “Solvable groups of finite non-Abelian sectional rank,” Ukr. Mat. Zh., 48, No. 3, 418–421 (1996).
B. Hartley, “Finite groups of automorphisms of locally soluble groups”, J. Algebra, 57, No. 1, 242–257 (1979).
D. I. Zaitsev, “On locally solvable groups of finite ranks”, Dokl. Akad. Nauk SSSR, 240, No. 2, 257–259 (1978).
V. P. Shunkov, “On locally finite groups with minimum condition for Abelian subgroups”, Algebra Logika, 9, No. 5, 579–615 (1970).
O. Yu. Dashkova, “Solvable groups of finite non-Abelian rank,” Ukr. Mat. Zh., 42, No. 2, 159–164 (1990).
M. Hall, Theory of Groups [Russian translation], Inostrannaya Literatura Moscow (1968).
V. V. Belyaev, “Locally finite groups with Chernikov Sylow p-subgroups”, Algebra Logika, 20, No. 6, 605–619 (1981).
I. I. Pavlyuk and V. P. Shunkov, “On locally finite groups with min-p condition for all p”, in: Abstracts of the VIIth All-Union Symposium on the Theory of Groups [in Russian], Krasnoyarsk University, Krasnoyarsk (1980), pp. 84–85.
O. Yu. Dashkova, Groups of Finite Metabelian Rank [in Russian], Preprint No. 90. I, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990).
O. Yu. Dashkova, “Locally almost solvable groups of finite non-Abelian rank” Ukr. Mat. Zh., 42, No. 4, 477–482 (1990).
P. H. Kropholler, “On finitely generated soluble groups with no large wreath products sections”, Proc. London Math. Soc., 49, No. 1, 155–169 (1984).
D. J. S. Robinson, “A note on groups of finite rank,” Compos. Math., 31, No. 2, 240–246 (1969).
D. I. Zaitsev, “On the theory of minimax groups,” Ukr. Mat. Zh., 23, No. 5, 652–660 (1971).
V. S. Charin, “On solvable groups of A4 type,” Mat. Sb., 53, No. 3, 895–914 (1960).
N. N. Myagkova, “On groups of finite rank,” Izv. Akad. Nauk SSSR, Ser. Mat., 13, No. 6, 495–512 (1949).
O. Yu. Dashkova, Groups of Finite Non-Abelian Rank [in Russian], Author's Abstract of Candidate-Degree Thesis (Physics and Mathematics). Novosibirsk (1990).
A. G. Kurosh, Theory of Groups [in Russian] Nauka, Moscow (1967).
Additional information
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1324–1331, October, 1997.
Rights and permissions
About this article
Cite this article
Dashkova, O.Y. Groups of finite non-Abelian sectional rank. Ukr Math J 49, 1494–1500 (1997). https://doi.org/10.1007/BF02487435
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487435