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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.


References [Enhancements On Off] (What's this?)

  • 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 $p$-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 $448,345,497,600$, 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

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