Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2013, Article ID 430870, 3 pages
http://dx.doi.org/10.1155/2013/430870
Research Article

On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

1School of Mathematics and Information Science, Yantai University, Yantai 264005, China
2Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Lyngby, Denmark

Received 3 August 2013; Accepted 11 September 2013

Academic Editors: J. Hoff da Silva and J. Park

Copyright © 2013 Jiangtao Shi and Cui Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Li and X. Zhao, “Finite groups with few non-cyclic subgroups,” Journal of Group Theory, vol. 10, no. 2, pp. 225–233, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Shi and C. Zhang, “Some results on nonnormal noncyclic subgroups of finite groups,” submitted.
  3. M. Kano, “On the number of conjugate classes of maximal subgroups in finite groups,” Japan Academy A, vol. 55, no. 7, pp. 264–265, 1979. View at Google Scholar · View at MathSciNet
  4. S. R. Li, “Finite groups having exactly two classes of nonnormal maximal subgroups of the same order,” Acta Mathematica Sinica, vol. 33, no. 3, pp. 388–392, 1990 (Chinese). View at Google Scholar · View at MathSciNet
  5. X. H. Li, “Finite groups having three maximal classes of subgroups of the same order,” Acta Mathematica Sinica, vol. 37, no. 1, pp. 108–115, 1994 (Chinese). View at Google Scholar
  6. W. J. Shi, “Finite groups having at most two classes of maximal subgroups,” Chinese Annals of Mathematics A, vol. 10, no. 5, pp. 532–537, 1989 (Chinese). View at Google Scholar
  7. D. J. S. Robinson, A Course in the Theory of Groups, Springer, New York, NY, USA, 2nd edition, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. H. Conway, R. T. Curtis, S. P. Norton et al., Atlas of Finite Groups, Clarendon Press, Oxford, UK, 1985.
  9. L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig, Germany, 1901.