Abstract
We study the structure of Sylow 2-subgroups in Shunkov periodic groups with almost layer-finite normalizers of finite nontrivial subgroups.
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S. N. Chernikov, “On the theory of infinite p-groups,” Dokl. Akad. Nauk SSSR, No. 1, 71–74 (1945).
S. I. Adyan, Burnside Problem and Identities in Groups [in Russian], Nauka, Moscow (1975).
A. Yu. Ol’shanskii, Geometry of Defining Relations in a Group [in Russian], Nauka, Moscow (1989).
V. I. Senashov, “Almost layer finiteness of the periodic part of a group without involutions,” Diskr. Mat., 14, No. 4, 133–152 (2002).
V. I. Senashov, “Sufficient conditions for the almost layer finiteness of groups,” Ukr. Mat. Zh., 51, No. 4, 472–485 (1999).
V. I. Senashov and V. P. Shunkov, “Almost layer finiteness of the periodic part of a group without involutions,” Diskr. Mat., 15, No. 3, 91–104 (2003).
V. P. Shunkov, “On the problem of minimality for locally finite groups,” Alg. Log., 9, No. 2, 220–248 (1970).
V. P. Shunkov, On Imbedding of Primary Elements in a Group [in Russian], Nauka, Novosibirsk (1992).
M. Hall, The Theory of Groups, Macmillan, New York (1959).
A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
V. P. Shunkov, “On periodic groups with some conditions of finiteness,” Dokl. Akad. Nauk SSSR, 195, No. 6, 1290–1293 (1970).
O. H. Kegel and B. A. F. Wehrfritz, Locally Finite Groups, North-Holland, Amsterdam (1973).
B. Hartley, “Finite groups of automorphisms of locally soluble groups,” J. Algebra, 57, No. 1, 242–257 (1979).
D. Gorenstein, Finite Groups, Harper and Row, New York (1968).
G. A. Malan’ina, “Semidirect products of cyclic groups,” Dokl. Akad. Nauk SSSR, 132, 762–765 (1960).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1548–1556, November, 2005.
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Senashov, V.I. On Sylow subgroups of Shunkov periodic groups. Ukr Math J 57, 1809–1817 (2005). https://doi.org/10.1007/s11253-006-0030-8
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DOI: https://doi.org/10.1007/s11253-006-0030-8