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
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.
- 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.
- N. Chigira and N. Iiyori, Prime graphs and Brauer characters, To appear in J. Group Theory.
- N. Chigira, N. Iiyori and H. Yamaki, Nonabelian Sylow subgroups of finite groups of even order, in preparation.
- Nobuo Iiyori, Sharp characters and prime graphs of finite groups, J. Algebra 163 (1994), no. 1, 1–8. MR 1257302, DOI https://doi.org/10.1006/jabr.1994.1001
- Nobuo Iiyori, A conjecture of Frobenius and the simple groups of Lie type. IV, J. Algebra 154 (1993), no. 1, 188–214. MR 1201919, DOI https://doi.org/10.1006/jabr.1993.1011
- Nobuo Iiyori and Hiroyoshi Yamaki, On a conjecture of Frobenius, Bull. Amer. Math. Soc. (N.S.) 25 (1991), no. 2, 413–416. MR 1102753, DOI https://doi.org/10.1090/S0273-0979-1991-16084-2
- Nobuo Iiyori and Hiroyoshi Yamaki, A conjecture of Frobenius and the simple groups of Lie type. III, J. Algebra 145 (1992), no. 2, 329–332. MR 1144935, DOI https://doi.org/10.1016/0021-8693%2892%2990105-U
- Sugaku Expositions, American Mathematical Society, Providence, RI, 1996. A translation of Sūgaku; Sugaku Expositions 9 (1996), no. 1. MR 1401603
- Nobuo Iiyori and Hiroyoshi Yamaki, Prime graph components of the simple groups of Lie type over the field of even characteristic, J. Algebra 155 (1993), no. 2, 335–343. MR 1212233, DOI https://doi.org/10.1006/jabr.1993.1048
- A. S. Kondrat′ev, On prime graph components of finite simple groups, Mat. Sb. 180 (1989), no. 6, 787–797, 864 (Russian); English transl., Math. USSR-Sb. 67 (1990), no. 1, 235–247. MR 1015040
- J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), no. 2, 487–513. MR 617092, DOI https://doi.org/10.1016/0021-8693%2881%2990218-0
- Hiroyoshi Yamaki, A characterization of the Suzuki simple group of order $448, 345, 497,600$, J. Algebra 40 (1976), no. 1, 229–244. MR 409632, DOI https://doi.org/10.1016/0021-8693%2876%2990094-6
- Hiroyoshi Yamaki, A conjecture of Frobenius and the sporadic simple groups, Comm. Algebra 11 (1983), no. 22, 2513–2518. MR 733339, DOI https://doi.org/10.1080/00927878308822977
- Hiroyoshi Yamaki, A conjecture of Frobenius and the simple groups of Lie type. I, Arch. Math. (Basel) 42 (1984), no. 4, 344–347. MR 753355, DOI https://doi.org/10.1007/BF01246125
- 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.
- N. Chigira and N. Iiyori, Prime graphs and Brauer characters, To appear in J. Group Theory.
- N. Chigira, N. Iiyori and H. Yamaki, Nonabelian Sylow subgroups of finite groups of even order, in preparation.
- N. Iiyori, Sharp characters and prime graphs of finite groups, J. Algebra 163 (1994), 1–8.
- N. Iiyori, A conjecture of Frobenius and the simple groups of Lie type IV, J. Algebra 154 (1993), 188–214.
- N. Iiyori and H. Yamaki, On a conjecture of Frobenius, Bull. Amer. Math. Soc. 25 (1991), 413–416.
- N. Iiyori and H. Yamaki, A conjecture of Frobenius and the simple groups of Lie type III, J. Algebra 145 (1992), 329–332.
- N. Iiyori and H. Yamaki, A conjecture of Frobenius, Sugaku Expositions, Amer. Math. Soc. 9 (1996), 69–85.
- 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.
- A. S. Kondrat’ev, Prime graph components of finite simple groups, Math. USSR Sbornik 67 (1990), 235–247.
- J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), 487–513.
- H. Yamaki, A characterization of the Suzuki simple groups of order $448,345,497,600$, J. Algebra 40 (1976), 229–244.
- 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 87i:20033
- 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 87i:20032
Similar Articles
Retrieve articles in Electronic Research Announcements of the American Mathematical Society
with MSC (1991):
20D05,
20D06,
20D20
Retrieve articles in all journals
with MSC (1991):
20D05,
20D06,
20D20
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
