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Finite groups whose character degree graphs coincide with their prime graphs

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Abstract

In the literature, there are several graphs related to a finite group G. Two of them are the character degree graph, denoted by ΔG), and the prime graph ΓG), In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.

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References

  1. B. Huppert: Endliche Gruppen I. Die Grundlehren der Mathematischen Wissenschaften 134, Springer, Berlin, 1967. (In German.)

    Google Scholar 

  2. M. L. Lewis: Solvable groups whose degree graphs have two connected components. J. Group Theory 4 (2001), 255–275.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. L. Lewis, Q. Meng: Square character degree graphs yield direct products. J. Algebra 349 (2012), 185–200.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. L. Lewis, D. L. White: Connectedness of degree graphs of nonsolvable groups. J. Algebra 266 (2003), 51–76 (2003); corrigendum ibid. 290 (2005), 594–598.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. P. Morresi Zuccari: Character degree graphs with no complete vertices. J. Algebra 353 (2012), 22–30.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. L. White: Degree graphs of simple linear and unitary groups. Commun. Algebra 34 (2006), 2907–2921.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. S. Williams: Prime graph components of finite groups. J. Algebra 69 (1981), 487–513.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, 34134, Fatih, Istanbul, Turkey

    Temha Erkoç & Utku Yilmaztürk

  2. Department of Mathematics, Doğuş University, Hasanpaṣa Mah., Zeamet Sok. No: 21, 34722, Acıbadem, Istanbul, Turkey

    İsmail Ş. Güloğlu

Authors
  1. Temha Erkoç
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  2. Utku Yilmaztürk
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  3. İsmail Ş. Güloğlu
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Corresponding author

Correspondence to Temha Erkoç.

Additional information

The work of the second author was supported by Scientific Research Projects Coordination Unit of Istanbul University. The project number is 48029.

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Erkoç, T., Yilmaztürk, U. & Güloğlu, İ.Ş. Finite groups whose character degree graphs coincide with their prime graphs. Czech Math J 68, 647–656 (2018). https://doi.org/10.21136/CMJ.2018.0553-16

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  • DOI: https://doi.org/10.21136/CMJ.2018.0553-16

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