Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The order of a group of even order


Author: Hiroyoshi Yamaki
Journal: Proc. Amer. Math. Soc. 136 (2008), 397-402
MSC (2000): Primary 20D05, 20D06
DOI: https://doi.org/10.1090/S0002-9939-07-09118-6
Published electronically: October 25, 2007
MathSciNet review: 2358476
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We will give an estimation of the order of a group of even order by the order of the centralizer of an involution using the classification of finite simple groups.


References [Enhancements On Off] (What's this?)

  • 1. M. Aschbacher and G. Seitz, Involutions in Chevalley groups over fields of even order, Nagoya Math. J. 63 (1976), 1-91. MR 0422401 (54:10391)
  • 2. R. Brauer and K. A. Fowler, On groups of even order, Ann. Math. 62 (1955), 565-583. MR 0074414 (17:580e)
  • 3. N. Burgoyne and C. Williamson, Centralizers of involutions in Chevalley groups of odd characteristic, Mimeographed notes (1972).
  • 4. N. Chigira, N. Iiyori and H. Yamaki, Non-abelian Sylow subgroups of finite groups of even order, Invent. Math. 139 (2000), 525-539. MR 1738059 (2001c:20042)
  • 5. J. Conway, R. T. Curtis, S. Norton, R. Parker, and R. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985. MR 827219 (88g:20025)
  • 6. R. H. Dye, On the conjugacy classes of involutions of the simple orthogonal groups over perfect fields of characteristic two, J. Algebra 18 (1971), 414-425. MR 0276366 (43:2113)
  • 7. R. H. Dye, On the involution classes of the linear groups $ GL_n(K)$, $ SL_n(K)$, $ PGL_n(K)$, $ PSL_n(K)$ over fields of characteristic two, Math. Proc. Cambridge Phil. Soc. 72 (1972), 1-6. MR 0294519 (45:3589)
  • 8. R. H. Dye, On the conjugacy classes of involutions of the unitary groups $ U_m(K)$, $ SU_m(K)$, $ PU_m(K)$, $ PSU_m(K)$ over perfect fields of characteristic $ 2$, J. Algebra 24 (1973), 453-459. MR 0308287 (46:7401)
  • 9. K. Harada and M. Miyamoto, On the order of a group of even order, To appear in J. Algebra.
  • 10. B. Huppert and N. Blackburn, Finite Groups III, Springer-Verlag, Berlin, 1982. MR 662826 (84i:20001b)
  • 11. N. Iiyori and H. Yamaki, Prime graph components of the simple groups of Lie type over the fields of even characteristic, J. Algebra 155 (1993), 335-343. Corrigenda 181 (1996) 659. MR 1212233 (94e:05268)
  • 12. A. S. Kondrat'ev, Prime graph components of finite simple groups, Math. USSR Sbornik 67 (1990), 235-247. MR 1015040 (90h:20018)
  • 13. M. Suzuki, Group theory II, Springer-Verlag, Berlin, 1986. MR 815926 (87e:20001)
  • 14. J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), 487-513. MR 617092 (82j:20054)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20D05, 20D06

Retrieve articles in all journals with MSC (2000): 20D05, 20D06


Additional Information

Hiroyoshi Yamaki
Affiliation: Department of Mathematics, Kumamoto University, Kumamoto 860-8555 Japan
Address at time of publication: JICA, Maipu 1300, Piso 21, C1006ACT Buenos Aires, Argentina
Email: yamaki@gpo.kumamoto-u.ac.jp, yamaki.hiroyoshi@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-07-09118-6
Keywords: Finite simple groups, centralizers of involutions
Received by editor(s): August 15, 2006
Published electronically: October 25, 2007
Additional Notes: The author was supported in part by Grant-in-Aid for Scientific Research (No. 16540030), Japan Society for the Promotion of Science
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society