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2001 Kernel systems on finite groups
Paul Lescot
Nagoya Math. J. 163: 71-85 (2001).

Abstract

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.

Citation

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Paul Lescot. "Kernel systems on finite groups." Nagoya Math. J. 163 71 - 85, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1002.20012
MathSciNet: MR1854389

Subjects:
Primary: 20D99

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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