Advertisement

Monatshefte für Mathematik

, Volume 170, Issue 3–4, pp 305–310 | Cite as

Mutually permutable products and conjugacy classes

  • A. Ballester-BolinchesEmail author
  • John Cossey
  • Yangming Li
Article

Abstract

The question of how certain arithmetical conditions on the lengths of the conjugacy classes of a finite group G influence the group structure has been studied by several authors with many results available. The purpose of this paper is to analyse the restrictions imposed by the lengths of the conjugacy classes of some elements of the factors of a finite group GG 1 G 2 · · · G r , which is the product of the pairwise mutually permutable subgroups G 1, G 2, . . . , G r , on its structure. Some earlier results appear as corollaries of our main theorems.

Keywords

Finite groups Mutually permutable products Conjugacy classes 

Mathematics Subject Classification

20D10 20D20 20D40 20E45 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ballester-Bolinches A., Esteban-Romero R., Asaad M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin (2010)CrossRefGoogle Scholar
  2. 2.
    Beidleman H., Heineken J.C.: Mutually permutable subgroups and group classes. Arch. Math. (Basel) 85, 18–30 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chillag M., Herzog D.: On the length of the conjugacy classes of finite groups. J. Algebra 131, 110–125 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Doerk K., Hawkes T.: Finite Soluble Groups, vol. 4 of De Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin (1992)CrossRefGoogle Scholar
  6. 6.
    Huppert B.: Endliche Gruppen I vol. 134 of Grund Math Wiss. Springer, Berlin (1967)CrossRefGoogle Scholar
  7. 7.
    Liu X., Wang Y., Wei H.: Notes on the length of conjugacy classes of finite groups. J. Pure Appl. Algebra 196(1), 111–117 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Qian G.H., Wang Y.M.: A note on conjugacy class sizes in finite groups. Acta Math. Sinica (Chin. Ser.) 52(1), 125–130 (2009)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • A. Ballester-Bolinches
    • 1
    Email author
  • John Cossey
    • 2
  • Yangming Li
    • 3
  1. 1.Departament d’ÀlgebraUniversitat de ValènciaBurjassotSpain
  2. 2.Department of Mathematics, School of Mathematical ScienceThe Australian National UniversityCanberraAustralia
  3. 3.Department of MathematicsGuangdong University of EducationGuangzhouPeople’s Republic of China

Personalised recommendations