Formations of absolutely solvable groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 2006Publisher:University of Debrecen/ Debreceni EgyetemJournal:Publicationes Mathematicae Debrecen, volume 69, pages 391-400 (issn: 0033-3883,

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Authors: Szabó, Edit;

doi: 10.5486/pmd.2006.3485

Formations of absolutely solvable groups

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Abstract

A finite group \(G\) is said to be absolutely solvable if it has a chief series all of whose factors are absolutely irreducible modules over their prime field. The main result in this paper states that the class of absolutely solvable groups is a formation containing the supersolvable groups. This formation is not saturated neither closed for subgroups.

Keywords

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, finite solvable groups, absolutely irreducible representations, formations

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