\(\mathfrak {Z}\) -permutable subgroups of finite groups

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• 作者：A. A. Heliel ; A. Ballester-Bolinches ; R. Esteban-Romero…
• 关键词：Finite group ; \(p\) ; soluble group ; \(p\) ; supersoluble ; \(\mathfrak {Z}\) ; permutable subgroup ; Subnormal subgroup
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：179
• 期：4
• 页码：523-534
• 全文大小：434 KB
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  2.Ballester-Bolinches, A., Esteban-Romero, R.: On minimal non-supersoluble groups. Rev. Mat. Iberoam. 23(1), 127–142 (2007). doi:10.​4171/​RMI/​488 MathSciNet CrossRef MATH
  3.Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, de Gruyter Expositions in Mathematics, vol. 53. Walter de Gruyter, Berlin (2010). doi:10.​1515/​9783110220612
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  8.Heliel, A.A., Al-Gafri, T.M.: On conjugate-\({\mathfrak{{Z}}}\) -permutable subgroups of finite groups. J. Algebra Appl. 12(8), 1350060 (2013). doi:10.​1142/​S021949881350060​6 (14 pages)
  9.Heliel, A.A., Li, X., Li, Y.: On \({\mathfrak{{Z}}}\) -permutability of minimal subgroups of finite groups. Arch. Math. (Basel) 83, 9–16 (2004). doi:10.​1007/​s00013-004-1014-2 MathSciNet CrossRef MATH
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  14.Li, Y., Li, X.: \(\mathfrak{Z}\) -permutable subgroups and \(p\) -nilpotence of finite groups. J. Pure Appl. Algebra 202, 72–81 (2005). doi:10.​1016/​j.​jpaa.​2005.​01.​007 MathSciNet CrossRef MATH
  15.Li, Y., Wang, L., Wang, Y.: Finite groups with some \({\mathfrak{{Z}}}\) -permutable subgroups. Glasgow Math. J. 52, 145–150 (2010). doi:10.​1017/​S001708950999023​1 MathSciNet CrossRef MATH
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• 作者单位：A. A. Heliel (1) (2)
  A. Ballester-Bolinches (3)
  R. Esteban-Romero (4) (5)
  M. O. Almestady (1)
  
  1. Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
  2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt
  3. Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
  4. Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022, Valencia, Spain
  5. Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081

文摘

Let \(\mathfrak {Z}\) be a complete set of Sylow subgroups of a finite group \(G\), that is, a set composed of a Sylow \(p\)-subgroup of \(G\) for each \(p\) dividing the order of \(G\). A subgroup \(H\) of \(G\) is called \(\mathfrak {Z}\)-permutable if \(H\) permutes with all members of \(\mathfrak {Z}\). The main goal of this paper is to study the embedding of the \(\mathfrak {Z}\)-permutable subgroups and the influence of \(\mathfrak {Z}\)-permutability on the group structure.