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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

On the number of different prime divisors of element orders


Author: Alexander Moretó
Journal: Proc. Amer. Math. Soc. 134 (2006), 617-619
MSC (2000): Primary 20D60; Secondary 20D06
Posted: July 7, 2005
MathSciNet review: 2180876
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the number of different prime divisors of the order of a finite group is bounded by a polynomial function of the maximum of the number of different prime divisors of the element orders. This improves a result of J. Zhang.

References

  • 1. B. Huppert, ``Character Theory of Finite Groups", de Gruyter, Berlin/New York, 1998. MR 1645304 (99j:20011)
  • 2. I. M. Isaacs, ``Character Theory of Finite Groups", Academic Press, New York, 1976. MR 0460423 (57:417)
  • 3. T. M. Keller, A linear bound for $\rho(n)$, J. Algebra 178 (1995), 643-652. MR 1359907 (96m:20035)
  • 4. A. Moretó, G. Qian, W. Shi, Finite groups whose conjugacy class graphs have few vertices, to appear in Arch. Math.
  • 5. P. Ribenboim, ``The Book of Prime Number Records", Springer-Verlag, New York, 1988. MR 0931080 (89e:11052)
  • 6. J. Zhang, Arithmetical conditions on element orders and group structure, Proc. Amer. Math. Soc. 123 (1995), 39-44. MR 1239809 (95c:20033)

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Additional Information

Alexander Moretó
Affiliation: Departament d'Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: Alexander.Moreto@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08156-6
PII: S 0002-9939(05)08156-6
Received by editor(s): September 21, 2004
Posted: July 7, 2005
Additional Notes: This research was supported by the Programa Ramón y Cajal, the Spanish Ministerio de Ciencia y Tecnología, grant BFM2001-0180, and the FEDER
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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