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Monatshefte für Mathematik

, Volume 184, Issue 4, pp 641–648 | Cite as

On the supersoluble hypercentre of a finite group

  • Liyun Miao
  • Adolfo Ballester-BolinchesEmail author
  • Ramón Esteban-Romero
  • Yangming Li
Article

Abstract

We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of \({{\mathrm{O}}}^p(G)\) plays an important role. Some known results can be reproved and some others appear as corollaries of our main theorems.

Keywords

Finite group p-Supersoluble group S-semipermutable subgroup 

Mathematics Subject Classification

20D10 20D20 

Notes

Acknowledgments

A. Ballester-Bolinches and R. Esteban-Romero have been supported by the Grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad, Spain, and FEDER, European Union. A. Ballester-Bolinches and Y. Li have been supported by a project from the National Natural Science Foundation of China (NSFC, No. 11271085) and a project of Natural Science Foundation of Guangdong Province (No. 2015A030313791). L. Miao thanks the China Scholarship Council and for its financial support and the Department of Mathematics of the University of Valencia for its hospitality.

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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  • Liyun Miao
    • 1
  • Adolfo Ballester-Bolinches
    • 2
    • 3
    Email author
  • Ramón Esteban-Romero
    • 3
    • 4
  • Yangming Li
    • 2
    • 3
  1. 1.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsGuangdong University of EducationGuangzhouPeople’s Republic of China
  3. 3.Departament de MatemàtiquesUniversitat de ValènciaValenciaSpain
  4. 4.Institut Universitari de Matemàtica Pura i AplicadaUniversitat Politècnica de ValènciaValenciaSpain

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