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Mutually permutable products and conjugacy classes

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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 G = G 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.

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References

  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)

    Book  Google Scholar 

  2. Beidleman H., Heineken J.C.: Mutually permutable subgroups and group classes. Arch. Math. (Basel) 85, 18–30 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chillag M., Herzog D.: On the length of the conjugacy classes of finite groups. J. Algebra 131, 110–125 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Doerk K., Hawkes T.: Finite Soluble Groups, vol. 4 of De Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin (1992)

    Book  Google Scholar 

  6. Huppert B.: Endliche Gruppen I vol. 134 of Grund Math Wiss. Springer, Berlin (1967)

    Book  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain

    A. Ballester-Bolinches

  2. Department of Mathematics, School of Mathematical Science, The Australian National University, Canberra, 0200, Australia

    John Cossey

  3. Department of Mathematics, Guangdong University of Education, Guangzhou, 510310, People’s Republic of China

    Yangming Li

Authors
  1. A. Ballester-Bolinches
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  2. John Cossey
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  3. Yangming Li
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Corresponding author

Correspondence to A. Ballester-Bolinches.

Additional information

Communicated by J. S. Wilson.

Dedicated to Professor Hermann Heineken on his 75th birthday.

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Ballester-Bolinches, A., Cossey, J. & Li, Y. Mutually permutable products and conjugacy classes. Monatsh Math 170, 305–310 (2013). https://doi.org/10.1007/s00605-012-0411-z

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  • DOI: https://doi.org/10.1007/s00605-012-0411-z

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