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

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Abstract | References | Similar Articles | Additional Information

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.

**1.**N. Chigira, Finite groups whose abelian subgroups have consecutive orders, Osaka J. Math.**35**(1998), 439-445.**2.**N. Chigira, Number of Sylow subgroups and -nilpotence of finite groups, J. Algebra**201**(1998), 71-85. CMP**98:09****3.**N. Chigira and N. Iiyori, Prime graphs and Brauer characters, To appear in J. Group Theory.**4.**N. Chigira, N. Iiyori and H. Yamaki, Nonabelian Sylow subgroups of finite groups of even order, in preparation.**5.**N. Iiyori, Sharp characters and prime graphs of finite groups, J. Algebra**163**(1994), 1-8. MR**94m:20021****6.**N. Iiyori, A conjecture of Frobenius and the simple groups of Lie type IV, J. Algebra**154**(1993), 188-214. MR**94d:20014****7.**N. Iiyori and H. Yamaki, On a conjecture of Frobenius, Bull. Amer. Math. Soc.**25**(1991), 413-416. MR**92e:20014****8.**N. Iiyori and H. Yamaki, A conjecture of Frobenius and the simple groups of Lie type III, J. Algebra**145**(1992), 329-332. MR**93c:20033****9.**N. Iiyori and H. Yamaki, A conjecture of Frobenius, Sugaku Expositions, Amer. Math. Soc.**9**(1996), 69-85. MR**97a:00046****10.**N. Iiyori and H. Yamaki, Prime graph components of the simple groups of Lie type over the fields of even characteristic, J. Algebra**155**(1993), 335-343; Corrigenda,**181**(1996), 659. MR**94e:05268****11.**A. S. Kondrat'ev, Prime graph components of finite simple groups, Math. USSR Sbornik**67**(1990), 235-247. MR**90h:20018****12.**J. S. Williams, Prime graph components of finite groups, J. Algebra**69**(1981), 487-513. MR**82j:20054****13.**H. Yamaki, A characterization of the Suzuki simple groups of order , J. Algebra**40**(1976), 229-244. MR**53:13384****14.**H. Yamaki, A conjecture of Frobenius and the sporadic simple groups I, Comm. Algebra**11**(1983), 2513-2518; II, Math. Comp.**46**(1986), 609-611; Supplement. Math. Comp.**46**(1986), S43-S46. MR**85k:20049**; MR**87i:20033****15.**H. Yamaki, A conjecture of Frobenius and the simple groups of Lie type I, Arch. Math.**42**(1984), 344-347; II, J. Algebra**96**(1985), 391-396. MR**85j:20010**; MR**87i:20032**

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

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