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

DOI:
https://doi.org/10.1090/S1079-6762-98-00051-1

Published electronically:
November 10, 1998

MathSciNet review:
1661753

Full-text PDF Free Access

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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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- N. Chigira, Finite groups whose abelian subgroups have consecutive orders, Osaka J. Math.
**35** (1998), 439–445.
- N. Chigira, Number of Sylow subgroups and $p$-nilpotence of finite groups, J. Algebra
**201** (1998), 71–85.
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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

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