On the membership problem of finite groups in solvably saturated formations.
type: Item
instance of: scholarly article
title: On the membership problem of finite groups in solvably saturated formations.
zbMATH Open document ID: 1272.20012
DOI: 10.1134/S0001434612090234
author: L. P. Avdashkova
author: S. F. Kamornikov
published in: Mathematical Notes
publication date: 2013-01-09T00:00:00Z
review text: All groups considered in this paper are finite. A formation \(\mathcal F\) is a solvably saturated formation if every group \(G\) having a solvable normal subgroup \(N\) for which \(G/\Phi(N)\in\mathcal F\) belongs to \(\mathcal F\). The main result in the paper is the following: Let \(\mathcal H\) be a solvably saturated subformation of a solvably saturated formation \(\mathcal F\). Let \(N\) be a solvable normal subgroup of a group \(G\), where \(G/N\in\mathcal F\). If every \(G\)-chief factor of \(F(G)/\Phi(G)\) is \(\mathcal H\)-central in \(G\), then \(G\in\mathcal F\).
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 6123761
zbMATH Keywords: finite groups
zbMATH Keywords: solvably saturated formations
zbMATH Keywords: c-normal subgroups
zbMATH Keywords: Frattini extensions
zbMATH Keywords: chief factors
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6123761