Abstract
A complete classification of finite biprimary groups in which every 3-maximal subgroup is \({\mathfrak{U}}\)-subnormal is given.
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References
Huppert B.: Normalteiler und maximale Untergruppen endlicher Gruppen. Math. Z. 60, 409–434 (1954)
Asaad M.: Finite groups some whose n-maximal subgroups are normal. Acta Math. Hungar. 54, 9–27 (1989)
R. Schmidt, Endliche Gruppen mit vielen modularen Untergruppen, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 34 (1969), 115–125.
W. Guo, Yu. V. Lutsenko and A. N. Skiba, On nonnilpotent groups with every two 3-maximal subgroups permutable, Siberian Math. J., 50 (2009), 988–997.
Yu. V. Lutsenko and A. N. Skiba, Finite groups with subnormal second and third maximal subgroups, Math. Notes, 91 (2012), 680–688.
V. N. Kniahina and V. S. Monakhov, On the permutability of n-maximal subgroups with Schmidt subgroups, Trudy Inst. Mat. i Mekh. UrO RAN, 18 (2012), 125–130.
V. A. Kovaleva and A. N. Skiba, Finite soluble groups with all n-maximal subgroups \({\mathfrak{F}}\)-subnormal, J. Group Theory, 17 (2014), 273–290.
V. A. Kovaleva and X. Yi, Finite groups with all 3-maximal subgroups K-\({\mathfrak{U}}\)-subnormal, arXiv:1406.3464v1 [math.GR].
Doerk K.: Minimal nicht uberauflosbare, endliche Gruppen. Math. Z. 91, 198–205 (1966)
K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter (Berlin–New York, 1992).
A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer-Verlag (Dordrecht, 2006).
B. Huppert, Endliche Gruppen I, Springer-Verlag (Berlin–Heidelberg–New York, 1967).
M. Weinstein (ed.), etc, Between Nilpotent and Solvable, Polygonal Publishing House (Passaic N.J., 1982).
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Research of Xiaolan Yi is supported by a NNSF grant of China (Grant # 11101369) and the Science Foundation of Zhejiang Sci–Tech University under grant 1013843-Y.
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Kovaleva, V.A., Yi, X. Finite biprimary groups with all 3-maximal subgroups \({\mathfrak{U}}\)-subnormal. Acta Math. Hungar. 146, 47–55 (2015). https://doi.org/10.1007/s10474-015-0498-5
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DOI: https://doi.org/10.1007/s10474-015-0498-5