Abstract
In this note, we give two new conditions for a finite group to be \(p\)-nilpotent under the assumption that all subgroups with an any fixed order are \(E\)-\(S\)-supplemented, and some recent results are generalized.
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Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of Finite Groups. Walter de Gruyter, Berlin (2010)
Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: Sufficient conditions for supersolubility of finite groups. J. Pure Appl. Algebra 127, 113–118 (1998)
Gorenstein, D.: Finite Groups. Chelsea, New York (1980)
Guo, X., Shum, K.P.: On \(c\)-normal maximal and minimal subgroups of Sylow \(p\)-subgroups of finite groups. Arch. Math. 80, 561–569 (2003)
Huppert, B.: Endliche Gruppen I. Springer, New York (1967)
Kegel, O.H.: Sylow-gruppen und abnormalteiler endlicher gruppen. Math. Z. 78, 205–221 (1962)
Kong, Q.: On an extension of the Frobenius\(^{\prime }\) theorem about \(p\)-nilpotency of a finite group. Monatsh. Math. 175, 133–138 (2014)
Li, Y., Wang, Y., Wei, H.: On \(p\)-nilpotency of finite groups with some subgroups \(\pi \)-quasinormally embedded. Acta Math. Hung. 108, 283–298 (2005)
Li, C., Zhang, X., Yi, X.: On \(E\)-\(S\)-supplemented subgroups of finite groups. Colloq. Math. 131, 41–51 (2013)
Li, C., Yu, X., Tang, N.: Finite \(p\)-supersoluble groups with some \(E\)-\(S\)-supplemented subgroups. Rend. Sem. Mat. Univ. Padova 133, 1–10 (2015)
Miao, L.: On weakly \(S\)-permutable subgroups. Bull. Braz. Math. Soc. New Ser. 41, 223–235 (2010)
Skiba, A.N.: On weakly \(S\)-permutable subgroups of finite groups. J. Algebra 315, 192–209 (2007)
Wang, Y.: On \(c\)-normality and its properties. J. Algebra 180, 954–965 (1996)
Wei, X., Guo, X.: On \(S\)-permutable subgroups and \(p\)-nilpotency of finite groups. Comm. Algebra 37, 3410–3417 (2009)
Wei, X., Guo, X.: On finite groups with prime-power order \(S\)-quasinormally embedded subgroups. Monatsh. Math. 162, 329–339 (2011)
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Communicated by J. S. Wilson.
The project is supported by the Natural Science Foundation of China (No: 11401264) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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Li, C., Huang, J. & Hu, B. A note on \(p\)-nilpotency of finite groups. Monatsh Math 179, 253–258 (2016). https://doi.org/10.1007/s00605-015-0733-8
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DOI: https://doi.org/10.1007/s00605-015-0733-8