Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T23:46:49.754Z Has data issue: false hasContentIssue false
  • English
  • Français

Families of solvable Frobenius subgroups in finite groups

Published online by Cambridge University Press:  22 January 2016

Paul Lescot
Paul Lescot*
Affiliation:
INSSET-Université de Picardie, 48 Rue Raspail, 02100 Saint-Quentin, France, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We introduce the notion of abelian system on a finite group G, as a particular case of the recently defined notion of kernel system (see this Journal, September 2001). Using a famous result of Suzuki on CN-groups, we determine all finite groups with abelian systems. Except for some degenerate cases, they turn out to be special linear group of rank 2 over fields of characteristic 2 or Suzuki groups. Our ideas were heavily influenced by [1] and [8].

Keywords

20D6020E28
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 165 , March 2002 , pp. 117 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Bender, H. and Glauberman, G., Local analysis for the Odd Order Theorem, Cambridge University Press, Cambridge, 1994.Google Scholar
[2] Herstein, I. N., A remark on finite groups, Proc. Amer. Math. Soc., 9 (1958), 255–257.Google Scholar
[3] Lescot, P., A note on CA-groups, Communications in Algebra, 18 (1990), no. 3, 833–838.Google Scholar
[4] Lescot, P., Kernel systems on finite groups, Nagoya Mathematical Journal, 163 (2001), 71–85.Google Scholar
[5] Scott, W. R., Group Theory, Dover, New York, 1987.Google Scholar
[6] Suzuki, M., Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., 99 (1961), 425–470.Google Scholar
[7] Suzuki, M., On a class of doubly transitive groups, Ann. of Math., 75 (1962), 105–145.CrossRefGoogle Scholar
[8] Thompson, J. G., Letter (August 31st, 1990).Google Scholar
[9] Weisner, L., Groups in which the normalizer of every element except identity is abelian, Bull. Amer. Math. Soc., 33 (1925), 413–416.Google Scholar