On the Shemetkov problem for Fitting classes.
type: Item
instance of: scholarly article
title: On the Shemetkov problem for Fitting classes.
zbMATH Open document ID: 1125.20010
author: Baojun Li
author: Wenbin Guo
published in: Beiträge zur Algebra und Geometrie
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://eudml.org/doc/224765
full work available at URL: 22.html
review text: The paper under review deals with Fitting classes of finite groups, that is, classes which are closed under subnormal subgroups and normal products. More precisely, it answers a question proposed by L. A. Shemetkov about local Fitting classes, which are Fitting classes defined by means of Hartley functions, dualising the concept of local formation. If \(\pi\) is a set of primes and \(F\) is a local Fitting class, it is proved that the class \(K_\pi(F)\) of all finite \(\pi\)-soluble groups with a Hall \(\pi\)-subgroup in \(F\) is a local Fitting class. As a consequence, a description of the \(F\)-radical of a finite \(\pi\)-soluble group is obtained.
reviewed by: Adolfo Ballester-Bolinches
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 5152755
zbMATH Keywords: finite groups
zbMATH Keywords: local Fitting classes
zbMATH Keywords: Hartley functions
zbMATH Keywords: finite \(\pi\)-soluble groups
zbMATH Keywords: Hall subgroups
zbMATH Keywords: radicals
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5152755