Annali di Matematica Pura ed Applicata (1923 -)

, Volume 194, Issue 1, pp 77–86 | Cite as

On a class of generalised Schmidt groups

  • A. Ballester-Bolinches
  • R. Esteban-Romero
  • Qinhui Jiang
  • Xianhua Li
Article

Abstract

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An \(A_5\)-free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

Keywords

Finite groups Nilpotent groups Maximal subgroups 

Mathematics Subject Classification (2010)

20D05 20D10 20F16 

Notes

Acknowledgments

The first and second authors have been supported by the Research Grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovación of Spain. The first author has also been supported by a project of the National Natural Science Foundation of China (No. 11271085). The third author has been supported by the China Postdoctoral Science Foundation funded project (No. 20100480582) and National Natural Science Foundation of China (No. 11101258). The fourth author has been supported by the National Natural Science Foundation of China (No. 11171243) and University of Jinan Research Funds for Doctors (XBS1335, XBS1336).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. Ballester-Bolinches
    • 1
  • R. Esteban-Romero
    • 1
    • 2
  • Qinhui Jiang
    • 3
    • 4
  • Xianhua Li
    • 5
  1. 1.Departament d’ÀlgebraUniversitat de ValènciaBurjassotSpain
  2. 2.Institut Universitari de Matemàtica Pura i AplicadaUniversitat Politècnica de ValènciaValènciaSpain
  3. 3.School of Mathematical SciencesUniversity of JinanJinanChina
  4. 4.Department of MathematicsShanghai UniversityShanghaiChina
  5. 5.School of Mathematical ScienceSoochow UniversitySuzhouChina

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