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On the structure of a mutually permutable product of finite groups

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Abstract

Let a finite group \({G = AB}\) be the product of the mutually permutable subgroups A and B. We investigate the structure of G given by conditions on conjugacy class sizes of elements in \({A \cup B}\) . Some recent results are extended.

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References

  1. A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin, New-York, 2010).

  2. Ballester-Bolinches A., Cossey J., Li Y.-M.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Camina A.R., Camina R.D.: The influence of conjugacy class sizes on the structure of finite groups: a survey. Asian-Eur. J. Math. 4, 559–588 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cossey J., Wang Y.: Remarks on the length of conjugacy classes of finite groups. Comm. Algebra. 27, 4347–4353 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. K. Doerk and T. O. Hawkes, Finite Soluble Groups, De Gruyter (Berlin, 1992).

  6. Felipe M.J., Martínez-Pastor A., Ortíz-Sotomayor V.M.: Square-free class sizes in mutually permutable products. J. Algebra 491, 190–206 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. I. M. Isaacs, Character Theory of Finite Groups, Academic Press (New York, 1976).

  8. Qian G., Wang Y.: On class size of p-singular elements in finite groups. Comm. Algebra 37, 1172–1181 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Qian G., Wang Y.: On conjugacy class sizes and character degrees of finite groups. J. Algebra Appl. 13, 1–8 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Michler G.O.: A finite simple group of Lie type has p-blocks with different defects, \({p \not = 2}\) , . J. Algebra 104, 220–230 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, School of Mathematical Science, The Australian National University, Canberra, 2601, Australia

    J. Cossey

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

    Y.-M. Li

Authors
  1. J. Cossey
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  2. Y.-M. Li
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Corresponding author

Correspondence to Y.-M. Li.

Additional information

The second author has been supported by the project of NSF of China (11271085), NSF of Guangdong Province (China) (2015A030313791) and The Innovative Team Project of Guangdong Province (China) (2014KTSCX196).

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Cossey, J., Li, YM. On the structure of a mutually permutable product of finite groups. Acta Math. Hungar. 154, 525–529 (2018). https://doi.org/10.1007/s10474-018-0796-9

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  • DOI: https://doi.org/10.1007/s10474-018-0796-9

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