We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.
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References
B. Huppert, “Normalteiler und maximale Untergruppen endlicher Gruppen,” Math. Z., 60, 409–434 (1954).
Z. Janko, “Finite groups with invariant fourth maximal subgroups,” Math. Z., 82, 82–89 (1963).
Z. Janko, “Finite simple groups with short chains of subgroups,” Math. Z., 84, 428–437 (1964).
R. K. Agrawal, “Generalized center and hypercenter of a finite group,” Proc. Amer. Math. Soc., 54, 13–21 (1976).
A. Mann, “Finite groups whose n-maximal subgroups are subnormal,” Trans. Amer. Math. Soc., 132, 395–409 (1968).
M. Asaad, “Finite groups some of whose n-maximal subgroups are normal,” Acta Math. Hung., 54, No. 1-2, 9–27 (1989).
L. A. Shemetkov, Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
Yu. V. Lutsenko and A. N. Skiba, “Finite nonnilpotent groups with normal or S-quasinormal n-maximal subgroups,” Izv. Gomel Univ., No. 1(52), 134–138 (2009).
M. Suzuki, “The nonexistence of a certain type of simple groups of odd order,” Proc. Amer. Math. Soc., 8, No. 4, 686–695 (1957).
Z. Janko, “Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen,” Math. Z., 79, 422–424 (1962).
O. H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen,” Math. Z., 78, 205–221 (1962).
D. Gorenstein, Finite Groups, Harper and Row, New York (1968).
B. Huppert, Endliche Gruppen. I, Springer, Berlin (1967).
M. Hall, Jr., The Theory of Groups, Macmillan, New York (1959).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 12, pp. 1630–1639, December, 2009.
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Lutsenko, Y.V., Skiba, A.N. Structure of finite groups with S-quasinormal third maximal subgroups. Ukr Math J 61, 1915–1922 (2009). https://doi.org/10.1007/s11253-010-0322-x
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DOI: https://doi.org/10.1007/s11253-010-0322-x