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Kernel systems on finite groups

Published online by Cambridge University Press:  22 January 2016

Paul Lescot
Paul Lescot*
Affiliation:
INSSET, Université de Picardie, de Picardie 48 Rue Raspail, 02100 Saint-Quentin, France, paul.lescot@insset.u-picardie.fr
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Abstract

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We introduce a notion of kernel systems on finite groups: roughly speaking, a kernel system on the finite group G consists in the data of a pseudo-Frobenius kernel in each maximal solvable subgroup of G, subject to certain natural conditions. In particular, each finite CA-group can be equipped with a canonical kernel system. We succeed in determining all finite groups with kernel system that also possess a Hall p′-subgroup for some prime factor p of their order; this generalizes a previous result of ours (Communications in Algebra 18(3), 1990, pp. 833-838). Remarkable is the fact that we make no a priori abelianness hypothesis on the Sylow subgroups.

Keywords

20E25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 71 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[1] Bender, H. and Glauberman, G., Local analysis for the Odd Order Theorem, Cambridge University Press, Cambridge, 1994.Google Scholar
[2] Burnside, W., On a class of groups of finite order, Trans. Camb. Phil. Soc., 18 (1900), 269–276.Google Scholar
[3] Kegel, O. H., Produkte nilpotenter Gruppen, Arch. Math., 12 (1961), 90–93.Google Scholar
[4] Lescot, P., A note on CA-groups, Communications in Algebra, 18 (1990), no. 3, 833–838.Google Scholar
[5] Scott, W. R., Group Theory, Dover, New York, 1987.Google Scholar
[6] Thompson, J. G., Letter (August 31st, 1990).Google Scholar
[7] Weisner, L., Groups in which the normalizer of every element except identity is abelian, Bull. Amer. Math. Soc., 33 (1925), 413–416.Google Scholar