Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON FINITE GROUPS WITH THE SAME ORDER TYPE AS SIMPLE GROUPS F4(q) WITH q EVEN

  • Received : 2020.09.21
  • Accepted : 2021.01.14
  • Published : 2021.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The main aim of this article is to study quantitative structure of finite simple exceptional groups F4(2n) with n > 1. Here, we prove that the finite simple exceptional groups F4(2n), where 24n + 1 is a prime number with n > 1 a power of 2, can be uniquely determined by their orders and the set of the number of elements with the same order. In conclusion, we give a positive answer to J. G. Thompson's problem for finite simple exceptional groups F4(2n).

Keywords

References

  1. S. H. Alavi, A. Daneshkhah, and H. Parvizi Mosaed, On quantitative structure of small Ree groups, Comm. Algebra 45 (2017), no. 9, 4099-4108. https://doi.org/10.1080/00927872.2016.1260730
  2. S. H. Alavi, A. Daneshkhah, and H. Parvizi Mosaed, Finite groups of the same type as Suzuki groups, Int. J. Group Theory 8 (2019), no. 1, 35-42. https://doi.org/10.22108/ijgt.2017.21556
  3. G. Chen, On structure of Frobenuis group and 2-Frobenuis group, J. Southwest China Normal Univ. 20 (2005), no. 5, 485-487.
  4. Z. M. Chen and W. J. Shi, On simple Cpp groups, J. Southwest China Teachers Univ. 18 (1993), no. 3, 249-256.
  5. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Eynsham, 1985.
  6. G. Frobenius, Verallgemeinerung des sylowschen satze, Berliner Sitz, 1895.
  7. A. S. Kondrat'ev, On prime graph components of finite simple groups, Mat. Sb. 180 (1989), no. 6, 787-797.
  8. V. D. Mazurov and E. I. Khukhro, The Kourovka notebook, Russian Academy of Sciences Siberian Division, Institute of Mathematics, Novosibirsk, 2006.
  9. C. Shao, W. Shi, and Q. Jiang, Characterization of simple K4-groups, Front. Math. China 3 (2008), no. 3, 355-370. https://doi.org/10.1007/s11464-008-0025-x
  10. J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), no. 2, 487-513. https://doi.org/10.1016/0021-8693(81)90218-0
  11. A. V. Zavarnitsine, Recognition of the simple groups L3(q) by element orders, J. Group Theory 7 (2004), no. 1, 81-97. https://doi.org/10.1515/jgth.2003.044