The order of a group of even order
Author:
Hiroyoshi Yamaki
Journal:
Proc. Amer. Math. Soc. 136 (2008), 397402
MSC (2000):
Primary 20D05, 20D06
Published electronically:
October 25, 2007
MathSciNet review:
2358476
Fulltext PDF Free Access
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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.
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 M. Aschbacher and G. Seitz, Involutions in Chevalley groups over fields of even order, Nagoya Math. J. 63 (1976), 191. MR 0422401 (54:10391)
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 R. Brauer and K. A. Fowler, On groups of even order, Ann. Math. 62 (1955), 565583. MR 0074414 (17:580e)
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 N. Burgoyne and C. Williamson, Centralizers of involutions in Chevalley groups of odd characteristic, Mimeographed notes (1972).
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 N. Chigira, N. Iiyori and H. Yamaki, Nonabelian Sylow subgroups of finite groups of even order, Invent. Math. 139 (2000), 525539. MR 1738059 (2001c:20042)
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 J. Conway, R. T. Curtis, S. Norton, R. Parker, and R. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985. MR 827219 (88g:20025)
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 R. H. Dye, On the conjugacy classes of involutions of the simple orthogonal groups over perfect fields of characteristic two, J. Algebra 18 (1971), 414425. MR 0276366 (43:2113)
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 R. H. Dye, On the involution classes of the linear groups , , , over fields of characteristic two, Math. Proc. Cambridge Phil. Soc. 72 (1972), 16. MR 0294519 (45:3589)
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 R. H. Dye, On the conjugacy classes of involutions of the unitary groups , , , over perfect fields of characteristic , J. Algebra 24 (1973), 453459. MR 0308287 (46:7401)
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 A. S. Kondrat'ev, Prime graph components of finite simple groups, Math. USSR Sbornik 67 (1990), 235247. MR 1015040 (90h:20018)
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 J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), 487513. MR 617092 (82j:20054)
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Additional Information
Hiroyoshi Yamaki
Affiliation:
Department of Mathematics, Kumamoto University, Kumamoto 8608555 Japan
Address at time of publication:
JICA, Maipu 1300, Piso 21, C1006ACT Buenos Aires, Argentina
Email:
yamaki@gpo.kumamotou.ac.jp, yamaki.hiroyoshi@gmail.com
DOI:
http://dx.doi.org/10.1090/S0002993907091186
PII:
S 00029939(07)091186
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 GrantinAid 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.
