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.

**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 , , , 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 , , , over perfect fields of characteristic*, 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)**

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.