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On the number of different prime divisors of element orders
Author(s):
Alexander
Moretó
Journal:
Proc. Amer. Math. Soc.
134
(2006),
617-619.
MSC (2000):
Primary 20D60;
Secondary 20D06
Posted:
July 7, 2005
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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:
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- 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
 , 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:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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