On \({\mathfrak F}\)-critical groups
type: Item
instance of: scholarly article
title: On \({\mathfrak F}\)-critical groups
zbMATH Open document ID: 0830.20036
author: Adolfo Ballester-Bolinches
author: M. D. Pérez-Ramos
published in: Journal of Algebra
publication date: 1996-01-21T00:00:00Z
review text: We say that a saturated formation \(\mathcal F\) has the Shemetkov property if every \(\mathcal F\)-critical group is either a Shmidt group or a cyclic group of prime order. The paper gives an exact description of the subgroup- closed saturated formations of soluble groups \(\mathcal F\) for which the Shemetkov property holds. With respect to the non-soluble case, the authors determine a necessary condition for a subgroup-closed saturated formation \(\mathcal F\) to have the Shemetkov property. Examples of subgroup- closed saturated formations with the Shemetkov property of a different nature are given.
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 783898
zbMATH Keywords: critical groups
zbMATH Keywords: Shemetkov property
zbMATH Keywords: Shmidt groups
zbMATH Keywords: cyclic groups
zbMATH Keywords: saturated formations of soluble groups
zbMATH Keywords: subgroup-closed saturated formations
reviewed by: Rodica Covaci
MaRDI profile type: Publication
full work available at URL: jabr.1995.1161
OpenAlex ID: W2038175343
DOI: 10.1006/JABR.1995.1161
description: scientific article; zbMATH DE number 783898