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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

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