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Monatshefte für Mathematik

, Volume 181, Issue 4, pp 753–760 | Cite as

On hall subnormally embedded subgroups of finite groups

  • Adolfo Ballester-Bolinches
  • John Cossey
  • ShouHong QiaoEmail author
Article
  • 174 Downloads

Abstract

A subgroup H of a finite group G is said to be Hall subnormally (respectively normally) embedded in G if there is a subnormal (respectively normal) subgroup N of G such that H is a Hall subgroup of N. The aim of this paper is to characterise the groups G having a Hall subnormally embedded subgroup of order |B| for each subgroup B of G. Some earlier results are consequences of our main theorem.

Keywords

Finite group Soluble group Hall subgroup Subnormal subgroup 

Mathematics Subject Classification

20D10 20D20 

Notes

Acknowledgments

The first author was supported by Proyecto MTM2014-54707-C3-1-P from Ministerio de Economía y Competitividad, Spain, and by Project from the National Natural Science Foundation of China (NSFC, No. 11271085). The third author was supported by Project from the National Natural Science Foundation of China (NSFC, No. 11201082), Cultivation Program for Outstanding Young College Teachers (Yq2013061) of Guangdong Province and Pei Ying Yu Cai Project of GDUT.

References

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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Departament d’ÀlgebraUniversitat de ValènciaBurjassotSpain
  2. 2.Mathematics Department, School of Mathematical ScienceThe Australian National UniversityCanberraAustralia
  3. 3.School of Applied MathematicsGuangdong University of TechnologyGuangzhouPeople’s Republic of China

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