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The incipient infinite cluster in high-dimensional percolation
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## Nonabelian Sylow subgroups of finite groups of even order

### Naoki Chigira, Nobuo Iiyori and Hiroyoshi Yamaki

**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.

*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`

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