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Nonabelian Sylow subgroups of finite groups of even order


Authors: Naoki Chigira, Nobuo Iiyori and Hiroyoshi Yamaki
Journal: Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 88-90
MSC (1991): Primary 20D05, 20D06, 20D20
Published electronically: November 10, 1998
MathSciNet review: 1661753
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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.


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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 1998 American Mathematical Society