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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.

Copyright 1998 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 88-90
• Publisher Identifier: S 1079-6762(98)00051-1
• 1991 Mathematics Subject Classification. Primary 20D05
• Key words and phrases.Sylow subgroups, prime graphs, simple groups
• Received by the editors October 20, 1997
• Posted on November 10, 1998
• Communicated by Efim Zelmanov
• Comments (When Available)

Naoki Chigira

Department of Mathematical Sciences, Muroran Institute of Technology, Hokkaido 050-8585, Japan

E-mail address: chigira@muroran-it.ac.jp

Nobuo Iiyori

Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8512, Japan

E-mail address: iiyori@po.yb.cc.yamaguchi-u.ac.jp

Hiroyoshi Yamaki

Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan

E-mail address: yamaki@gpo.kumamoto-u.ac.jp