We study the influence of the properties of supplemented subgroups on the structure of finite groups. The conditions under which a normal subgroup of a finite group possesses cyclic chief p-factors are obtained.
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References
S. N. Chernikov (editor), Groups with Constraints for Subgroups [in Russian], Naukova Dumka, Kiev (1971).
S. N. Chernikov, Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).
N. S. Chernikov, Groups Factorable in the Product of Permutable Subgroups [in Russian], Naukova Dumka, Kiev (1987).
O. Kegel, “Sylow-Gruppen and Subnormalteiler endlicher Gruppen,” Math. Z., 78, 205–221 (1962).
A. Ballester-Bolinches and M. C. Pedraza-Aguilera, “Sufficient conditions for supersolvability of finite groups,” J. Pure Appl. Algebra, 127, 113–118 (1988).
K. A. Al-Sharo and O. Shemetkova, “An application of the concept of a generalized central element,” Algebra Discr. Math., 4, 1–10 (2007).
A. N. Skiba, “On the SE-core of subgroups of a finite group,” Probl. Fiz. Mat. Tekhn., 4, No. 5, 39–45 (2010).
A. N. Skiba, “On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups,” J. Group Theory, 13, 841–850 (2010).
O. L. Shemetkova, “On finite groups with Q-central elements of prime order,” Tr. Inst. Mat. (Minsk), 16, No. 1, 97–99 (2008).
K. Doerk and T. Hawkes, Finite Soluble Groups, de Gruyter, New York (1992).
L. A. Shemetkov, Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
H. Kurzweil and B. Stellmacher, The Theory of Finite Groups: An Introduction, Springer, New York (2004).
I. M. Isaacs, Finite Group Theory, American Mathematical Society, Providence, RI (2008).
B. Huppert, Endliche Gruppen I, Springer, Berlin (1967).
W. E. Deskins, “On quasinormal subgroups of finite groups,” Math. Z., 82, 125–132 (1963).
P. Schmid, “Subgroups permutable with all Sylow subgroups,” J. Algebra, 82, 285–293 (1998).
O. L. Shemetkova, “Finite groups with a system of generalized central elements,” Algebra Discr. Math., 4, 59–71 (2004).
K. A. Al-Sharo, E. A. Molokova, and L. A. Shemetkov, “Factorizable groups and formations,” Acta Appl. Math., 85, 3–10 (2005).
F. Gross, “Conjugacy of odd Hall subgroups,” Bull. London Math. Soc., 19, 311–319 (1987).
N. Ito, “A note on (LM) -groups of finite orders,” Kodai Math. Semin. Repts., 1-2, 1–6 (1951).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 9, pp. 1227–1235, September, 2013.
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Xiaolan, Y., Shemetkova, O.L. Finite Groups with System of SE-Supplemented Subgroups. Ukr Math J 65, 1363–1372 (2014). https://doi.org/10.1007/s11253-014-0864-4
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DOI: https://doi.org/10.1007/s11253-014-0864-4