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Nonabelian Sylow subgroups of finite groups of even order
Author(s):
Naoki
Chigira;
Nobuo
Iiyori;
Hiroyoshi
Yamaki
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
88-90.
MSC (1991):
Primary 20D05, 20D06, 20D20
Posted:
November 10, 1998
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Abstract:
We have been able to prove that every nonabelian Sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution. The proof depends upon the consequences of the classification of finite simple groups.
References:
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Additional Information:
Naoki
Chigira
Affiliation:
Department of Mathematical Sciences, Muroran Institute of Technology, Hokkaido 050-8585, Japan
Email:
chigira@muroran-it.ac.jp
Nobuo
Iiyori
Affiliation:
Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8512, Japan
Email:
iiyori@po.yb.cc.yamaguchi-u.ac.jp
Hiroyoshi
Yamaki
Affiliation:
Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan
Email:
yamaki@gpo.kumamoto-u.ac.jp
DOI:
10.1090/S1079-6762-98-00051-1
PII:
S 1079-6762(98)00051-1
Keywords:
Sylow subgroups,
prime graphs,
simple groups
Received by editor(s):
October 20, 1997
Posted:
November 10, 1998
Additional Notes:
The third author was supported in part by Grant-in-Aid for Scientific Research (No. 8304003, No. 08640051), Ministry of Education, Science, Sports and Culture, Japan.
Communicated by:
Efim Zelmanov
Copyright of article:
Copyright
1998,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article N. Chigira and N. Iiyori, Prime graphs and Brauer characters, J. Group Theory 1 (1998), 363--368.
N. Chigira, N. Iiyori and H. Yamaki, Non-abelian Sylow subgroups of finite groups of even order, Invent. Math. 139 (2000), 525--539.
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