A \({\mathfrak{U}_m}\) -subnormal subgroup of a finite group

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• 作者：V. A. Vasilyev
• 关键词：finite group ; $${\mathfrak{U}_m}$$ U m ; subnormal subgroup ; modular subgroup ; solubly saturated formation ; p ; nilpotent group ; supersoluble subgroup ; 20D10 ; 20D15 ; 20D20
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：148
• 期：1
• 页码：117-131
• 全文大小：678 KB
• 参考文献：1.W. Guo, A. N. Skiba and N. Yang, A generalized CAP-subgroup of a finite group, Sci. China Math., 58 (2015), doi:10.​1007/​s11425-015-5005-5 .
  2.R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter (Berlin, 1994).
  3.Guo W., Skiba A. N.: On some classes of finite quasi-\({\mathfrak{F}}\) -groups. J. Group Theory 12, 407–417 (2009)MathSciNet CrossRef MATH
  4.A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin–New York, 2010).
  5.M. Weinstein (ed.), et. al., Between Nilpotent and Solvable, Polygonal Publishing House (Passaic, 1982).
  6.Asaad M.: Finite groups with certain subgroups of Sylow subgroups complemented. J. Algebra 323, 1958–1965 (2010)MathSciNet CrossRef MATH
  7.W. Guo, A.N. Skiba and N. Yang, SE-supplemented subgroups of finite groups, Rend. Sem. Mat. Padova, 129 (2013), 245–263.
  8.Li B.: On \({\Pi}\) -property and \({\Pi}\) -normality of subgroups of finite groups. J. Algebra 334, 321–337 (2011)MathSciNet CrossRef MATH
  9.L. A. Shemetkov and A. N. Skiba, On the \({\mathfrak{X}\Phi}\) -hypercentre of finite groups, J. Algebra, 322 (2009), 2106–2117.
  10.Skiba A. N.: On two questions of L.A. Shemetkov concerning hypercyclically embedded subgroups of finite groups. J. Group Theory 13, 841–850 (2010)MathSciNet CrossRef MATH
  11.A. N. Skiba, A characterization of the hypercyclically embedded subgroups of finite groups, J. Pure Appl. Algebra, 215 (2011), 257–261.
  12.A. N. Skiba, Cyclicity conditions for G-chief factors of normal subgroups of a group G, Siberian Math. Journal, 52 (2011), 127–130 (in Russian).
  13.Kegel O. H.: Zur Struktur mehrfach faktorisierbarer endlicher Gruppen. Math. Z. 87, 409–434 (1965)MathSciNet CrossRef
  14.A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer (Dordrecht, 2006).
  15.K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter (Berlin–New York, 1992).
  16.B. Huppert, Endliche Gruppen I, Springer-Verlag (Berlin–Heidelberg–New York, 1967).
  17.Chen X., Guo W., Skiba A. N.: Some conditions under which a finite group belongs a Baer local formation. Comm. Algebra 42, 4188–4205 (2014)MathSciNet CrossRef MATH
  18.D. Gorenstein, Finite Groups, Harper & Row Publishers (New York, Evanston, London, 1968).
  19.T. M. Gagen, Topics in Finite Groups, London Mathematical Society Lecture Note Series, vol. 16, Cambridge University Press (Cambridge, 1976).
  20.W. Guo and A. N. Skiba, On the intersection of the F-maximal subgroups and the generalized \({\mathfrak{F}}\) -hypercentre of a finite group, J. Algebra, 366 (2012), 112–125.
  21.Thompson J. G.: Normal p-complements of finite groups. J. Algebra 1, 43–46 (1964)MathSciNet CrossRef MATH
  22.A. N. Skiba, A characterization of hypercyclically embedded subgroups of finite groups, J. Pure Appl. Algebra, 215 (2011), 257–261.
  23.Wang Y.: c-Normality of groups and its properties. J. Algebra 180, 954–965 (1996)MathSciNet CrossRef MATH
  24.A. Ballester-Bolinches and Y. Wang, Finite groups with some C-normal minimal subgroups, J. Pure Appl. Algebra, 153 (2000), 121–127.
  25.Skiba A. N.: A note on c-normal subgroups of finite groups. Algebra Discrete Math. 3, 85–95 (2005)MathSciNet
  26.D. Li and X. Guo, The influence of c-normality of subgroups on the structure of finite groups II, Comm. Algebra, 26 (1998), 1913–1922.
  27.Wei H.: On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups. Comm. Algebra 29, 2193–2200 (2001)MathSciNet CrossRef MATH
  28.H. Wei, Y. Wang and Y. Li, On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups II, Comm. Algebra, 31 (2003), 4807–4816.
  29.J. J. Jaraden and A. N. Skiba, On c-normal subgroups of finite groups, Comm. Algebra, 35 (2007), 3776–3788.
  30.M. Ramadan, M. Ezzat Mohamed and A. A. Heliel, On c-normality of certain subgroups of prime power order of finite groups, Arch. Math., 85 (2005), 203–210.
  31.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)MathSciNet CrossRef MATH
  
• 作者单位：V. A. Vasilyev (1)
  
  1. Department of Mathematics, Francisk Skorina Gomel State University, 246019, Gomel, Belarus
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632

文摘

A \({\mathfrak{U}_m}\)-subnormal subgroup of a finite group is introduced, some new characterizations of the hypercyclically embedded subgroups of a finite group are obtained and a series of known results is generalized. Mathematics Subject Classification 20D10 20D15 20D20