Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 2, pp. 533-540 (2009)

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Three remarks on absolutely solvable groups

Péter P. Pálfy

Alfréd Rényi Institute of Mathematics and Eötvös University, H--1364 Budapest, P.O.Box 127, Hungary, e-mail: ppp{@}

Abstract: First, we characterize finite groups that are not absolutely solvable, but every proper subgroup of them is absolutely solvable. Second, we show that every hereditary absolutely solvable group of odd order is an M-group. Third, we exhibit examples of groups which are not absolutely solvable, although they can be written as a product of two absolutely solvable normal subgroups.

Keywords: solvable group, chief series, absolutely irreducible representation, M-group, Fitting class

Classification (MSC2000): 20D10

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Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.

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